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Recursive Formulas (recursive + formula)
Selected AbstractsStability and identification for rational approximation of frequency response function of unbounded soilEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2010Xiuli Du Abstract Exact representation of unbounded soil contains the single output,single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency-domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped-parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least-squares fitting problem using the hybrid genetic-simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil,structure-interaction examples. Copyright © 2009 John Wiley & Sons, Ltd. [source] COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELSMATHEMATICAL FINANCE, Issue 4 2005Berend Roorda The framework of coherent risk measures has been introduced by Artzner et al. (1999; Math. Finance 9, 203,228) in a single-period setting. Here, we investigate a similar framework in a multiperiod context. We add an axiom of dynamic consistency to the standard coherence axioms, and obtain a representation theorem in terms of collections of multiperiod probability measures that satisfy a certain product property. This theorem is similar to results obtained by Epstein and Schneider (2003; J. Econ. Theor. 113, 1,31) and Wang (2003; J. Econ. Theor. 108, 286,321) in a different axiomatic framework. We then apply our representation result to the pricing of derivatives in incomplete markets, extending results by Carr, Geman, and Madan (2001; J. Financial Econ. 32, 131,167) to the multiperiod case. We present recursive formulas for the computation of price bounds and corresponding optimal hedges. When no shortselling constraints are present, we obtain a recursive formula for price bounds in terms of martingale measures. [source] The probability that similar haplotypes are identical by descentANNALS OF HUMAN GENETICS, Issue 3 2002I. M. NOLTE The logic of gene mapping in highly penetrant diseases is to find the minimal overlap of haplotypes that are identical by descent (IBD). If the pedigree is unknown, identity by descent of haplotype overlap cannot be established with certainty. In many cases, it is intuitively clear that similar haplotypes are indeed IBD. The logical and statistical evaluation of haplotype overlap requires that probabilities of IBD are substantial. It is, therefore, important to estimate these probabilities. In this paper, we derive a recursive formula for the probability of IBD. Simulations are used to validate the expected values and to study the variability around the expected value. We demonstrate that for populations 1000 generations of age , without bottlenecks , haplotypes of 1 cM consisting of at least five microsatellite markers have a significant probability to be IBD. Likewise, SNP haplotypes of 1 cM should consist of at least nine identical SNP alleles for a similar probability of IBD. Without considering bottlenecks, haplotypes consisting of as few as three SNPs spanning a region of less than 0.01 cM are likely IBD in populations that are 10000 generations of age. [source] Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Seppo Järvenpää Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A digital predistorter for wireless transmittersINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 4 2009D. Bondar Abstract A novel digital baseband predistorter with improved reduction of spectral regrowth is proposed and investigated. The improvements are achieved by using a proposed predistortion technique and extended power amplifier (PA) fundamental-frequency modeling. The digital baseband predistortion (DPD), known for its simplicity of realization, low cost and integrability; however, it suffers from poor linearizing performances. We incorporate baseband iterative injection of in-band distortion components into the baseband DPD to enhance the nonlinearity compensation. General formulas for the fundamental-frequency output of a PA with n -order nonlinearity and recursive formulas for calculating the injected components for different number of iterations are developed. The proposed iterative digital baseband predistorter is verified experimentally with a wireless PA and measured results are presented to demonstrate feasibility of the proposed concept. The spectral regrowth suppression of 20 dB is achieved for a 3.5 MHz digitally modulated signal. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source] State-space Models with Finite Dimensional DependenceJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2001Christian Gourieroux We consider nonlinear state-space models, where the state variable (,t) is Markov, stationary and features finite dimensional dependence (FDD), i.e. admits a transition function of the type: ,(,t|,t,1) =,(,t)a,(,t)b(,t,1), where ,(,t) denotes the marginal distribution of ,t, with a finite number of cross-effects between the present and past values. We discuss various characterizations of the FDD condition in terms of the predictor space and nonlinear canonical decomposition. The FDD models are shown to admit explicit recursive formulas for filtering and smoothing of the observable process, that arise as an extension of the Kitagawa approach. The filtering and smoothing algorithms are given in the paper. JEL. C4. [source] THE DEPENDENCE STRUCTURE OF RUNNING MAXIMA AND MINIMA: RESULTS AND OPTION PRICING APPLICATIONSMATHEMATICAL FINANCE, Issue 1 2010Umberto Cherubini We provide general results for the dependence structure of running maxima (minima) of sets of variables in a model based on (i) Markov dynamics; (ii) no Granger causality; (iii) cross-section dependence. At the time series level, we derive recursive formulas for running minima and maxima. These formulas enable to use a "bootstrapping" technique to recursively recover the pricing kernels of barrier options from those of the corresponding European options. We also show that the dependence formulas for running maxima (minima) are completely defined from the copula function representing dependence among levels at the terminal date. The result is applied to multivariate discrete barrier digital products. Barrier Altiplanos are simply priced by (i) bootstrapping the price of univariate barrier products; (ii) evaluating a European Altiplano with these values. [source] COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELSMATHEMATICAL FINANCE, Issue 4 2005Berend Roorda The framework of coherent risk measures has been introduced by Artzner et al. (1999; Math. Finance 9, 203,228) in a single-period setting. Here, we investigate a similar framework in a multiperiod context. We add an axiom of dynamic consistency to the standard coherence axioms, and obtain a representation theorem in terms of collections of multiperiod probability measures that satisfy a certain product property. This theorem is similar to results obtained by Epstein and Schneider (2003; J. Econ. Theor. 113, 1,31) and Wang (2003; J. Econ. Theor. 108, 286,321) in a different axiomatic framework. We then apply our representation result to the pricing of derivatives in incomplete markets, extending results by Carr, Geman, and Madan (2001; J. Financial Econ. 32, 131,167) to the multiperiod case. We present recursive formulas for the computation of price bounds and corresponding optimal hedges. When no shortselling constraints are present, we obtain a recursive formula for price bounds in terms of martingale measures. [source] | ||||||||||