This article is cited in 4 papers

Estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary

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 statistical method for estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary is proposed. The considered functional defines the probability representation of the solution of the corresponding parabolic first boundary value problem. The problem posed is solved by the numerical solution of stochastic differential equations (SDE) by the Euler method. The evaluation of an error of the proposed method is derived, and estimations of variance of the obtained parametric derivatives are given. Some numerical results are presented.

Key words: diffusion process, stochastic differential equations, absorbing boundary, derivatives with respect to parameters, Euler method.

UDC: 519.676

Received: 24.12.2007
Revised: 14.01.2008

 English version: Numerical Analysis and Applications, 2008, 1:4, 314–331