This article is cited in 1 paper

Solving SDE's numerically to estimate parametric derivatives of the solution to a parabolic boundary value problem with a Neumann boundary condition

S. A. Gusev

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: In this paper, a parabolic boundary value problem with a Neumann boundary condition is considered. The diffusion process with reflection from the boundary corresponds to the boundary problem. A statistical method to estimate the solution and parametric derivatives of the considered problem is proposed. This method is based on solving SDE's by the Euler method. The order of convergence of the obtained estimates is established. The results of numerical computations are presented.

Key words: parabolic boundary value problem, reflected diffusion, parametric derivatives, stochastic differential equations, Euler method.

UDC: 519.676

Received: 01.06.2006
Revised: 08.08.2006