Home About us Contact
|
Home About us Contact | ||
|
|
||
Stochastic Representation (stochastic + representation)
Selected AbstractsImpact of climate change on runoff from a mid-latitude mountainous catchment in central JapanHYDROLOGICAL PROCESSES, Issue 10 2009Yoshinori Shinohara Abstract Hydrologic balance in high-altitude, mid-latitude mountain areas is important in terms of the water resources available to associated lowlands. This study examined how current and historical shifts in precipitation (P) patterns and concurrent increases in temperature (T) affected runoff (Q) and other hydrologic components in a mid-latitude mountain catchment of central Japan, using a combination of long-term data and a simplified hydrologic model, along with their stochastic treatment. The availability of intensive meteorological and hydrological data from the period 1997,2001 allowed the derivation of key relationships for the current climate that tie the forcing term to the parameters or state variables. By using the data recorded in the period 1965,2001, the force for driving the historical simulation was generated. Based on this model and historical shifts in P and T, the probability density functions of Q (pdf(Q)) was computed. A main novelty in this study is that such a stochastic representation, which is useful for considering the influence of projected shifts in environmental factors on the hydrologic budget, was provided. Despite the large increase in the rate of T in winter and spring, pdf(Q) in spring and summer varied appreciably during the time studied mainly because of an increase in snowmelt. An interannual change in whole-year Q was robust to shifts in T because while Q in spring increased, in summer it decreased, implying a crucial effect of global warming on mountain hydrologic regimes is change in the timing of Q. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stochastic Response of a Continuous System with Stochastic Surface Irregularities to an Accelerated LoadPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003C.A. Schenk The problem of calculating the second moment characteristics of the response of a general class of nonconservative linear distributed parameter systems with stochastically varying surface roughness, excited by a moving concentrated load, is investigated. In particular the case of an accelerated load is discussed. The surface roughness is modeled as a Gaussian stationary second order process. For the stochastic representation of the surface roughness a orthogonal series expansion of the covariance kernel, the so called Karhunen-Loéve expansion, is applied. The resulting initial/boundary value problem is transformed by eigenfunction expansion into the modal state space. Second moment characteristics of the response are determined numerically by direct integration using a Runge-Kutta method. [source] Can error source terms in forecasting models be represented as Gaussian Markov noises?THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005C. Nicolis Abstract The repercussions of model error on the long term climatological means and on the variability around them are analysed. The extent to which a stochastic representation of error source terms provides a universal correcting mechanism is addressed. General relations are derived linking the model error to the climatological means and the variability properties of a forecasting model subjected to a correcting Gaussian Markov noise on the basis of moment equations associated with Fokker,Planck and Liouville type equations. These relations are implemented in a variety of models giving rise to regular and to chaotic solutions. As it turns out, forecasting models fall into distinct universality classes differing in their response to the effect of noise according to the structure of the Jacobian and the Hessian matrices of the model phase-space velocity. It is concluded that different trends may exist in which the ,correcting' noise tends to depress or, on the contrary, amplify the model error. Copyright © 2005 Royal Meteorological Society. [source] Second-order backward stochastic differential equations and fully nonlinear parabolic PDEsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2007Patrick Cheridito For a d -dimensional diffusion of the form dXt = ,(Xt)dt + ,(Xt)dWt and continuous functions f and g, we study the existence and uniqueness of adapted processes Y, Z, ,, and A solving the second-order backward stochastic differential equation (2BSDE) If the associated PDE has a sufficiently regular solution, then it follows directly from Itô's formula that the processes solve the 2BSDE, where ,, is the Dynkin operator of X without the drift term. The main result of the paper shows that if f is Lipschitz in Y as well as decreasing in , and the PDE satisfies a comparison principle as in the theory of viscosity solutions, then the existence of a solution (Y, Z,,, A) to the 2BSDE implies that the associated PDE has a unique continuous viscosity solution v and the process Y is of the form Yt = v(t, Xt), t , [0, T]. In particular, the 2BSDE has at most one solution. This provides a stochastic representation for solutions of fully nonlinear parabolic PDEs. As a consequence, the numerical treatment of such PDEs can now be approached by Monte Carlo methods. © 2006 Wiley Periodicals, Inc. [source] | ||||||||||