This article is cited in 2 papers

Minimizing the variance of estimate of mathematical expectation of a diffusion process functional by parametric transformation of the parabolic boundary value problem

S. A. Gusev

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

Abstract: This paper is associated with finding the ways of reducing the variance of the estimate of mathematical expectation of the functional of a diffusion process moving in a domain with an absorbing boundary. The estimate of mathematical expectation of the functional is obtained using a numerical solution of stochastic differential equations (SDE's) by the Euler method. A formula of the limiting variance at decreasing the integration step in the Euler method is obtained. A method of reducing the variance value of the estimate based on transformation of the parabolic boundary value problem corresponding to the diffusion process is proposed. Some numerical results are presented.

Key words: diffusion process, stochastic differential equations, absorbing boundary, variance of an estimate of the functional, Euler method.

UDC: 519.676

Received: 15.01.2010
Revised: 28.06.2010

 English version: Numerical Analysis and Applications, 2011, 4:2, 114–124

Bibliographic databases:

•