Информационная система "Конференции"

Abstracts

Stochastic simulation and Monte-Carlo methods

Let us consider the Cauchy problem (without boundaries and with the Dirichlet boundary conditions) for stochastic partial differential equation of the form $$ frac{displaystylepartial^2 U}{displaystylepartial t^2}(t,x) - a^2frac{displaystylepartial^2 U}{displaystylepartial x^2}(t,x) = g(t,x,U)+ f(t,x,U),W(t,x), quad x in R, ; t in R^+, $$ where $W$ is a Gaussian white noise on the plane. For the wave equation when $g$ and $f$ do not depend on $U$, we develop an efficient algorithm to construct realizations of $U$ [1]. For Klein-Gordon equation ($g=c U(t,x)$, $f=const$) we propose several numerical methods as well. The numerical methods are based on integral representations for the corresponding stochastic differential equations. vspace{8mm} 1. A.~Martin, S.M.~Prigarin, and G.~Winkler. Numerical simulation for the linear stochastic wave equation. Preprint 01-23, IBB, GSF Neuherberg, 2001, 14p.

Note. Abstracts are published in author's edition

Mail to Webmaster

|Home Page| |English Part|

Go to Home