Weak approximation of stochastic differential delay equations

被引：26

作者：

Buckwar, E

Shardlow, T

机构：

[1] Humboldt Univ, Inst Math, Bereich Stochast, D-10099 Berlin, Germany

[2] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2005年 / 25卷 / 01期

关键词：

theoretical approximation of solutions; stochastic partial differential equations; stochastic delay equations; stability and convergence of numerical approximations;

D O I：

10.1093/imanum/drh012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A numerical method for a class of Ito stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parametrized by its time step. Weak convergence with respect to a class of smooth test functionals is established by using the infinite-dimensional version of the Kolmogorov equation. With regularity assumptions on coefficients and initial data, the rate of convergence is shown to be proportional to the time step. Some computations are presented to demonstrate the rate of convergence.

引用

页码：57 / 86

页数：30

共 28 条

[1]

[Anonymous], STUD CERC MAT

[2]

[Anonymous], 1990, ENCY MATH APPL

[3]

[Anonymous], STUD CERC MAT

[4]

Baker C. T. H., 2000, Electronic Transactions on Numerical Analysis, V11