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## Brownian Motion (brownian + motion)
Kinds of Brownian Motion
## Selected Abstracts## Impact of the Sampling Rate on the Estimation of the Parameters of Fractional Brownian Motion JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2006Zhengyuan ZhuPrimary 60G18; secondary 62D05, 62F12 Abstract., Fractional Brownian motion is a mean-zero self-similar Gaussian process with stationary increments. Its covariance depends on two parameters, the self-similar parameter H and the variance C. Suppose that one wants to estimate optimally these parameters by using n equally spaced observations. How should these observations be distributed? We show that the spacing of the observations does not affect the estimation of H (this is due to the self-similarity of the process), but the spacing does affect the estimation of the variance C. For example, if the observations are equally spaced on [0, n] (unit-spacing), the rate of convergence of the maximum likelihood estimator (MLE) of the variance C is . However, if the observations are equally spaced on [0, 1] (1/n -spacing), or on [0, n2] (n -spacing), the rate is slower, . We also determine the optimal choice of the spacing , when it is constant, independent of the sample size n. While the rate of convergence of the MLE of C is in this case, irrespective of the value of ,, the value of the optimal spacing depends on H. It is 1 (unit-spacing) if H = 1/2 but is very large if H is close to 1. [source] ## Simulating a class of stationary Gaussian processes using the Davies,Harte algorithm, with application to long memory processes JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2003PETER F. CRAIGMILEWe demonstrate that the fast and exact Davies,Harte algorithm is valid for simulating a certain class of stationary Gaussian processes , those with a negative autocovariance sequence for all non-zero lags. The result applies to well known classes of long memory processes: Gaussian fractionally differenced (FD) processes, fractional Gaussian noise (fGn) and the nonstationary fractional Brownian Motion (fBm). [source] ## A Parametric Approach to Flexible Nonlinear Inference ECONOMETRICA, Issue 3 2001James D. HamiltonThis paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt=,(xt)+,t where the functional form of ,(,) is unknown. We propose viewing ,(,) itself as the outcome of a random process. The paper introduces a new stationary random field m(,) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for ,(,). We view the parameters that characterize the relation between a given realization of m(,) and the particular value of ,(,) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions ,(,). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment trade-off may explain the previously reported uneven empirical success of the Phillips Curve. [source] ## ADAPTIVE CONSTRAINTS AND THE PHYLOGENETIC COMPARATIVE METHOD: A COMPUTER SIMULATION TEST EVOLUTION, Issue 1 2002Emilia P. MartinsAbstract Recently, the utility of modern phylogenetic comparative methods (PCMs) has been questioned because of the seemingly restrictive assumptions required by these methods. Although most comparative analyses involve traits thought to be undergoing natural or sexual selection, most PCMs require an assumption that the traits be evolving by less directed random processes, such as Brownian motion (BM). In this study, we use computer simulation to generate data under more realistic evolutionary scenarios and consider the statistical abilities of a variety of PCMs to estimate correlation coefficients from these data. We found that correlations estimated without taking phylogeny into account were often quite poor and never substantially better than those produced by the other tested methods. In contrast, most PCMs performed quite well even when their assumptions were violated. Felsenstein's independent contrasts (FIC) method gave the best performance in many cases, even when weak constraints had been acting throughout phenotypic evolution. When strong constraints acted in opposition to variance-generating (i.e., BM) forces, however, FIC correlation coefficients were biased in the direction of those BM forces. In most cases, all other PCMs tested (phylogenetic generalized least squares, phylogenetic mixed model, spatial autoregression, and phylogenetic eigenvector regression) yielded good statistical performance, regardless of the details of the evolutionary model used to generate the data. Actual parameter estimates given by different PCMs for each dataset, however, were occasionally very different from one another, suggesting that the choice among them should depend on the types of traits and evolutionary processes being considered. [source] ## Bacterial motility: links to the environment and a driving force for microbial physics FEMS MICROBIOLOGY ECOLOGY, Issue 1 2006James G. MitchellAbstract Bacterial motility was recognized 300 years ago. Throughout this history, research into motility has led to advances in microbiology and physics. Thirty years ago, this union helped to make run and tumble chemotaxis the paradigm for bacterial movement. This review highlights how this paradigm has expanded and changed, and emphasizes the following points. The absolute magnitude of swimming speed is ecologically important because it helps determine vulnerability to Brownian motion, sensitivity to gradients, the type of receptors used and the cost of moving, with some bacteria moving at 1 mm s,1. High costs for high speeds are offset by the benefit of resource translocation across submillimetre redox and other environmental gradients. Much of environmental chemotaxis appears adapted to respond to gradients of micrometres, rather than migrations of centimetres. In such gradients, control of ion pumps is particularly important. Motility, at least in the ocean, is highly intermittent and the speed is variable within a run. Subtleties in flagellar physics provide a variety of reorientation mechanisms. Finally, while careful physical analysis has contributed to our current understanding of bacterial movement, tactic bacteria are increasingly widely used as experimental and theoretical model systems in physics. [source] ## Earnings-Based Bonus Compensation FINANCIAL REVIEW, Issue 4 2009António CâmaraG39; M52 Abstract This article studies the cost of contingent earnings-based bonus compensation. We assume that the firm has normal and abnormal earnings. The normal earnings result from normal firm activities and are modeled as an arithmetic Brownian motion. The abnormal earnings result from surprising activities (e.g., introduction of an unexpected new product, an unexpected strike) and are modeled as a compound Poisson process where the earnings jump sizes have a normal distribution. We investigate, in a simple general equilibrium model, how normal and abnormal earnings affect the cost of contingent bonus compensation to the firm. [source] ## Apparent/spurious multifractality of data sampled from fractional Brownian/Lévy motions HYDROLOGICAL PROCESSES, Issue 15 2010Shlomo P. NeumanAbstract Many earth and environmental variables appear to be self-affine (monofractal) or multifractal with spatial (or temporal) increments having exceedance probability tails that decay as powers of , , where 1 < , , 2. The literature considers self-affine and multifractal modes of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. We demonstrate theoretically that data having finite support, sampled across a finite domain from one or several realizations of an additive Gaussian field constituting fractional Brownian motion (fBm) characterized by , = 2, give rise to positive square (or absolute) increments which behave as if the field was multifractal when in fact it is monofractal. Sampling such data from additive fractional Lévy motions (fLm) with 1 < , < 2 causes them to exhibit spurious multifractality. Deviations from apparent multifractal behaviour at small and large lags are due to nonzero data support and finite domain size, unrelated to noise or undersampling (the causes cited for such deviations in the literature). Our analysis is based on a formal decomposition of anisotropic fLm (fBm when , = 2) into a continuous hierarchy of statistically independent and homogeneous random fields, or modes, which captures the above behaviour in terms of only E + 3 parameters where E is Euclidean dimension. Although the decomposition is consistent with a hydrologic rationale proposed by Neuman (2003), its mathematical validity is independent of such a rationale. Our results suggest that it may be worth checking how closely would variables considered in the literature to be multifractal (e.g. experimental and simulated turbulent velocities, some simulated porous flow velocities, landscape elevations, rain intensities, river network area and width functions, river flow series, soil water storage and physical properties) fit the simpler monofractal model considered in this paper (such an effort would require paying close attention to the support and sampling window scales of the data). Parsimony would suggest associating variables found to fit both models equally well with the latter. Copyright © 2010 John Wiley & Sons, Ltd. [source] ## Geometric Brownian motion as a model for river flows HYDROLOGICAL PROCESSES, Issue 7 2002Mario LefebvreAbstract Let X(t) be the flow of a certain river at time t. A geometric Brownian motion process is used as a model for X(t) and is found to give very good forecasts of future flows. The forecasted values generated by this one-dimensional model are compared with those provided by a deterministic model that requires the evaluation of 18 entries. Based on two important criteria, the stochastic model is superior, on average, to the deterministic model for forecasts up to 4 days ahead. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Solutions of linear and semilinear distributed parameter equations with a fractional Brownian motion INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2009T. E. DuncanAbstract In this paper, some linear and semilinear distributed parameter equations (equations in a Hilbert space) with a (cylindrical) fractional Brownian motion are considered. Solutions and sample path properties of these solutions are given for the stochastic distributed parameter equations. The fractional Brownian motions are indexed by the Hurst parameter H,,,(0, 1). For H,=,½ the process is Brownian motion. Solutions of these linear and semilinear equations are given for each H,,,(0, 1) with the assumptions differing for the cases H,,,(0, ½) and H,,,(½, 1). For the linear equations, the solutions are mild solutions and limiting Gaussian measures are characterized. For the semilinear equations, the solutions are either mild or weak. The weak solutions are obtained by transforming the measure of the associated linear equation by a Radon,Nikodym derivative (likelihood function). An application to identification is given by obtaining a strongly consistent family of estimators for an unknown parameter in a linear equation with distributed noise or boundary noise. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## The rate of learning-by-doing: estimates from a search-matching model JOURNAL OF APPLIED ECONOMETRICS, Issue 6 2010Julien PratWe construct and estimate by maximum likelihood a job search model where wages are set by Nash bargaining and idiosyncratic productivity follows a geometric Brownian motion. The proposed framework enables us to endogenize job destruction and to estimate the rate of learning-by-doing. Although the range of the observations is not independent of the parameters, we establish that the estimators satisfy asymptotic normality. The structural model is estimated using Current Population Survey data on accepted wages and employment durations. We show that it accurately captures the joint distribution of wages and job spells. We find that the rate of learning-by-doing has an important positive effect on aggregate output and a small impact on employment. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Acceleration of absolute negative mobility JOURNAL OF SEPARATION SCIENCE, JSS, Issue 10 2007Jan RegtmeierAbstract Recently, the counter intuitive migration phenomenon of absolute negative mobility (ANM) has been demonstrated to occur for colloidal particles in a suitably arranged post array within a microfluidic device [1]. This effect is based on the interplay of Brownian motion, nonlinear dynamics induced through microstructuring, and nonequilibrium driving, and results in a particle movement opposite to an applied static force. Simultaneously, the migration of a different particle species along the direction of the static force is possible [19], thus providing a new tool for particle sorting in microfluidic device format. The so far demonstrated maximum velocities for micrometer-sized spheres are slow, i. e., in the order of 10 nm per second. Here, we investigate numerically, how maximum ANM velocities can be significantly accelerated by a careful adjustment of the post size and shape. Based on this numerical analysis, a post design is developed and tested in a microfluidic device made of PDMS. The experiment reveals an order of magnitude increase in velocity. [source] ## Impact of the Sampling Rate on the Estimation of the Parameters of Fractional Brownian Motion JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2006Zhengyuan ZhuPrimary 60G18; secondary 62D05, 62F12 Abstract., Fractional Brownian motion is a mean-zero self-similar Gaussian process with stationary increments. Its covariance depends on two parameters, the self-similar parameter H and the variance C. Suppose that one wants to estimate optimally these parameters by using n equally spaced observations. How should these observations be distributed? We show that the spacing of the observations does not affect the estimation of H (this is due to the self-similarity of the process), but the spacing does affect the estimation of the variance C. For example, if the observations are equally spaced on [0, n] (unit-spacing), the rate of convergence of the maximum likelihood estimator (MLE) of the variance C is . However, if the observations are equally spaced on [0, 1] (1/n -spacing), or on [0, n2] (n -spacing), the rate is slower, . We also determine the optimal choice of the spacing , when it is constant, independent of the sample size n. While the rate of convergence of the MLE of C is in this case, irrespective of the value of ,, the value of the optimal spacing depends on H. It is 1 (unit-spacing) if H = 1/2 but is very large if H is close to 1. [source] ## The Limiting Density of Unit Root Test Statistics: A Unifying Technique JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2000Mithat GonenIn this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively. AMS 1991 subject classification. Primary 62M10; secondary 62E20. [source] ## Phylogenetic autocorrelation and heritability of geographic range size, shape and position of fiddler crabs, genus Uca (Crustacea, Decapoda) JOURNAL OF ZOOLOGICAL SYSTEMATICS AND EVOLUTIONARY RESEARCH, Issue 2 2010J. C. NaboutAbstract The aim of this study was to evaluate the levels of phylogenetic heritability of the geographical range size, shape and position for 88 species of fiddler crabs of the world, using phylogenetic comparative methods and simulation procedures to evaluate their fit to the neutral model of Brownian motion. The geographical range maps were compiled from literature, and range size was based on the entire length of coastline occupied by each species, and the position of each range was calculated as its latitudinal and longitudinal midpoint. The range shape of each species was based in fractal dimension (box-counting technique). The evolutionary patterns in the geographical range metrics were explored by phylogenetic correlograms using Moran's I autocorrelation coefficients, autoregressive method (ARM) and phylogenetic eigenvector regression (PVR). The correlograms were compared with those obtained by simulations of Brownian motion processes across phylogenies. The distribution of geographical range size of fiddler crabs is right-skewed and weak phylogenetic autocorrelation was observed. On the other hand, there was a strong phylogenetic pattern in the position of the range (mainly along longitudinal axis). Indeed, the ARM and PVR evidenced, respectively, that ca. 86% and 91% of the longitudinal midpoint could be explained by phylogenetic relationships among the species. The strong longitudinal phylogenetic pattern may be due to vicariant allopatric speciation and geographically structured cladogenesis in the group. The traits analysed (geographical range size and position) did not follow a Brownian motion process, thus suggesting that both adaptive ecological and evolutionary processes must be invoked to explain their dynamics, not following a simple neutral inheritance in the fiddler-crab evolution. Resumen El objetivo de este trabajo fue estimar los niveles de herencia filogenética existentes en la posición geográfica, forma y el tamaño de rango geográfico en 88 especies de cangrejo violinista del mundo, mediante simulaciones y métodos comparativos filogenéticos para así evaluar su ajuste al modelo neutro de evolución browniana. Los mapas de rango geográfico se obtuvieron de la literatura. La forma de rango geográfico fue estimada en la dimensión fractal. Los patrones evolutivos en el tamaño y forma del rango geográfico y la posición geográfica fueron explorados mediante correlogramas filogenéticos utilizando el índice I de Moran, coeficientes autorregresivos (ARM) y regressión por autovetores filogenéticos (PVR). Estos correlogramas fueron comparados con aquellos obtenidos mediante la simulación de procesos de evolución browniana en las filogenias. El tamaño y forma de rango geográfico del cangrejo violinista mostró una distribución apuntada hacia la derecha aunque no se encontró autocorrelación filogenética. Por otra parte, se observó un marcado patrón filogenético para la posición geográfica del rango (principalmente a lo largo del eje longitudinal). De hecho, el ARM y PVR evidenció respectivamente que cerca del 86% y 91% de la localización del punto medio longitudinal del rango se puede explicar mediante las relaciones filogenéticas existentes entre las especies. El fuerte patrón filogenético en la longitud podría ser debido a especiación alopátrica y a una cladogénesis estructurada geográficamente para el grupo, tal y como se propuso en las hipótesis. Los rasgos analizados (rango geográfico y posición geográfica) no siguieron un proceso de evolución browniana, sugiriendo pues que tanto los procesos evolutivos como la adaptación ecológica deberían ser tenidos en cuenta para explicar sus dinámicas, ya que el transcurso de la evolución del cangrejo violinista no se explica mediante un simple modelo de herencia neutra. [source] ## A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS MATHEMATICAL FINANCE, Issue 4 2006Ross A. MallerThis paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity. [source] ## Nonconvergence in the Variation of the Hedging Strategy of a European Call Option MATHEMATICAL FINANCE, Issue 4 2003R. Th.In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source] ## A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome MATHEMATICAL FINANCE, Issue 4 2003Yonggan ZhaoThis paper considers a portfolio problem with control on downside losses. Incorporating the worst-case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black-Scholes formula, a closed-form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model. [source] ## Robust Hedging of Barrier Options MATHEMATICAL FINANCE, Issue 3 2001Haydyn BrownThis article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion. We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight. [source] ## Time Changes for Lévy Processes MATHEMATICAL FINANCE, Issue 1 2001Hélyette GemanThe goal of this paper is to consider pure jump Lévy processes of finite variation with an infinite arrival rate of jumps as models for the logarithm of asset prices. These processes may be written as time-changed Brownian motion. We exhibit the explicit time change for each of a wide class of Lévy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Lévy processes that are analytically tractable, in their characteristic functions and Lévy densities, and hence are relevant for option pricing. [source] ## Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007Chunyan JiAbstract This paper discusses a randomized logistic equation (1) with initial value x(0)=x0>0, where B(t) is a standard one-dimension Brownian motion, and ,,(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Resolving Concentrated Particle Size Mixtures Using Dynamic Light Scattering PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION, Issue 3 2007Michael KaszubaAbstract Dynamic light scattering (DLS) is a technique used for measuring the size of molecules and particles undergoing Brownian motion by observing time-dependent fluctuations in the intensity of scattered light. The measurement of samples using conventional DLS instrumentation is limited to low concentrations due to the onset of a phenomenon called multiple scattering. The problems of multiple scattering have been addressed in a light scattering instrument incorporating non- invasive backscatter optics (NIBS). This novel optic arrangement maximizes the detection of scattered light while maintaining signal quality and allows for measurements of turbid samples. This paper discusses the ability of backscatter detection to accurately determine particle sizes at 1,%w/v sample concentrations and demonstrates the correct resolution of different size populations using a series of latex standard mixtures with known volume ratios. The concentration of 1,%w/v is much higher than can be measured on conventional dynamic light scattering instruments. [source] ## Analysis of Particle Size Distribution by Particle Tracking PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION, Issue 5 2004Christiane FinderAbstract Particle tracking is performed using a combination of dark field or fluorescence video microscopy with automatic image analysis. The optical detection together with the image analysis software allows for the time resolved localization of individual particles with diameters between 100 and 1000,nm. Observation of their Brownian motion over a set of time intervals leads to the determination of their mean square displacements under the given room temperature and viscosity. Hereby, the radii of a set of particles visible within a given optical frame are derived simultaneously. Rapid data analysis leads to reliable particle size histograms. The applicability of this method is demonstrated on polystyrene latices and PMMA nanospheres with radii between 51,nm and 202,nm. [source] ## The evolution of screening PHARMACOEPIDEMIOLOGY AND DRUG SAFETY, Issue 1 2001J. A. Muir Gray CBEBotany is usually considered to be the gentlest of sciences with botanists being regarded as people who study relatively safe specimens, compared with, for example, anthropologists or microbiologists. However, botanists have their moments, particularly when collecting new species. The great botanists of the eighteenth and nineteenth centuries risked their lives in collecting and bringing back species, which we now take for granted, and Robert Brown was one of these adventurers, a young Scot who accompanied Sir Joseph Banks to New Holland. It was not, however, for his adventurous lifestyle that Brown is remembered but for his startling observation of the movements of pollen grains on a microscope slide. He noted that the pollen grains were in perpetual agitated motion, without purpose or direction but full of energy. This motion, called Brownian motion, arises from the movement of molecules, and Brownian motion is the term that has been applied to much of healthcare, including many screening programmes, which have in the past been marked more by the amount of energy and activity than by a clear sense of direction or positive achievement. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Synchronized diapause termination of the peach twig borer Anarsia lineatella (Lepidoptera: Gelechiidae): Brownian motion with drift? PHYSIOLOGICAL ENTOMOLOGY, Issue 1 2010PETROS T. DAMOSThe course of diapause development is studied for the first time for Anarsia lineatella (Zeller) (Lepidoptera: Gelechiidae) under field and laboratory conditions for three successive years (2005,2007) in northern Greece. Photoperiod has a significant influence on diapause termination and the mean number of days to pupation decreases progressively throughout the winter season. Cold storage, for at least 30 days at 4°C, results in a synchronized reactivation of the larvae, with the developmental time of larvae chilled for 45 and 60 days at 4°C becoming significantly shorter. A theoretical stochastic description of the effect of chilling on diapause termination is attempted. Larvae have discrete ,physiological stages' with different degrees of diapause intensity, and the insect passes through those stages with a probability distribution S(t) that evolves over time. This pattern of progressive transition is similar to Brownian motion and finally leads to a successfully synchronized diapause break in spring. Hence, A. lineatella overwinters in a weak diapause state and may complete diapause development in late January, although it shows synchronized termination in early February, after the experience of essential chilling. [source] ## Forced Alveolar Flows and Mixing in the Lung PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009David BorerThe air flows deep inside the lung are not only important in gas exchange processes but they also determine the efficiency of particle deposition and retention. The study aims at quantifying the relative influence of different flow components in the transport of small particles in alveolar geometries such as convective breathing patterns, wall movement, gravitational settling and Brownian motion. In addition, the possibility and efficiency of external forcing is studied, relying on the mechanism of internal acoustic streaming. A viscous oscillating boundary layer flow is converted into a steady, viscosity-independent bulk motion which is very efficient at low Reynolds numbers. The streaming can be controlled by external parameters (excitation amplitude, frequency, beam shape) and may thus be of diagnostic and therapeutic relevance. Numerical simulations are performed to analyze the flow patterns in 3D model geometries and to measure deposition rates. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Numerical valuation of options under Kou's model PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Jari ToivanenArticle first published online: 6 AUG 200Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a linear complementarity problem (LCP) with the same operator. Spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit Rannacher scheme. For the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost. When pricing European options the resulting dense linear systems are solved using a stationary iteration. Also for pricing American options similar iterations can be employed. A numerical experiment demonstrates that the described method is very efficient as accurate option prices can be computed in a few milliseconds on a PC. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## The long-range electrostatic interactions control tRNA,aminoacyl-tRNA synthetase complex formation PROTEIN SCIENCE, Issue 6 2003Dmitry Tworowski3D, three-dimensional; PDB, Protein Data Bank of experimentally determined 3D structures of proteins; aaRS, aminoacyl-tRNA synthetase Abstract In most cases aminoacyl-tRNA synthetases (aaRSs) are negatively charged, as are the tRNA substrates. It is apparent that there are driving forces that provide a long-range attraction between like charge aaRS and tRNA, and ensure formation of "close encounters." Based on numerical solutions to the nonlinear Poisson-Boltzmann equation, we evaluated the electrostatic potential generated by different aaRSs. The 3D-isopotential surfaces calculated for different aaRSs at 0.01 kT/e contour level reveal the presence of large positive patches,one patch for each tRNA molecule. This is true for classes I and II monomers, dimers, and heterotetramers. The potential maps keep their characteristic features over a wide range of contour levels. The results suggest that nonspecific electrostatic interactions are the driving forces of primary stickiness of aaRSs,tRNA complexes. The long-range attraction in aaRS,tRNA systems is explained by capture of negatively charged tRNA into "blue space area" of the positive potential generated by aaRSs. Localization of tRNA in this area is a prerequisite for overcoming the barrier of Brownian motion. [source] ## Testing range estimators of historical volatility THE JOURNAL OF FUTURES MARKETS, Issue 3 2006Jinghong ShuThis study investigates the relative performance of various historical volatility estimators that incorporate daily trading range: M. Parkinson (1980), M. Garman and M. Klass (1980), L. C. G. Rogers and S. E. Satchell (1991), and D. Yang and Q. Zhang (2000). It is found that the range estimators all perform very well when an asset price follows a continuous geometric Brownian motion. However, significant differences among various range estimators are detected if the asset return distribution involves an opening jump or a large drift. By adding microstructure noise to the Monte Carlo simulation, the finding of S. Alizadeh, M. W. Brandt, and F. X. Diebold (2002),that range estimators are fairly robust toward microstructure effects,is confirmed. An empirical test with S&P 500 index return data shows that the variances estimated with range estimators are quite close to the daily integrated variance. The empirical results support the use of range estimators for actual market data. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:297,313, 2006 [source] ## The valuation of European options when asset returns are autocorrelated THE JOURNAL OF FUTURES MARKETS, Issue 1 2006Szu-Lang LiaoThis article derives the closed-form formula for a European option on an asset with returns following a continuous-time type of first-order moving average process, which is called an MA(1)-type option. The pricing formula of these options is similar to that of Black and Scholes, except for the total volatility input. Specifically, the total volatility input of MA(1)-type options is the conditional standard deviation of continuous-compounded returns over the option's remaining life, whereas the total volatility input of Black and Scholes is indeed the diffusion coefficient of a geometric Brownian motion times the square root of an option's time to maturity. Based on the result of numerical analyses, the impact of autocorrelation induced by the MA(1)-type process is significant to option values even when the autocorrelation between asset returns is weak. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:85,102, 2006 [source] ## Option pricing with a non-zero lower bound on stock price THE JOURNAL OF FUTURES MARKETS, Issue 8 2005Ming DongBlack, F. and Scholes, M. (1973) assume a geometric Brownian motion for stock prices and therefore a normal distribution for stock returns. In this article a simple alternative model to Black and Scholes (1973) is presented by assuming a non-zero lower bound on stock prices. The proposed stock price dynamics simultaneously accommodate skewness and excess kurtosis in stock returns. The feasibility of the proposed model is assessed by simulation and maximum likelihood estimation of the return probability density. The proposed model is easily applicable to existing option pricing models and may provide improved precision in option pricing. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:775,794, 2005 [source] |