Weak approximation of stochastic differential delay equations

Evelyn Buckwar; Tony Shardlow

doi:10.1093/imanum/drh012

Weak approximation of stochastic differential delay equations

Evelyn Buckwar, Tony Shardlow

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

A numerical method for a class of Itô 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.

Original language	English
Pages (from-to)	57-86
Number of pages	30
Journal	IMA Journal of Numerical Analysis
Volume	25
Issue number	1
DOIs	https://doi.org/10.1093/imanum/drh012
Publication status	Published - 1 Jan 2005

Keywords

Stability and convergence of numerical approximations
Stochastic delay equations
Stochastic partial differential equations
Theoretical approximation of solutions

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics
Computational Mathematics

Access to Document

10.1093/imanum/drh012

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abstract = "A numerical method for a class of It{\^o} 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.",

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AB - A numerical method for a class of Itô 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.

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KW - Stochastic partial differential equations

KW - Theoretical approximation of solutions

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