Weak approximation of stochastic differential delay equations

Evelyn Buckwar, Tony Shardlow

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)57-86
Number of pages30
JournalIMA Journal of Numerical Analysis
Volume25
Issue number1
DOIs
Publication statusPublished - 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

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