Weak convergence of the Euler scheme for stochastic differential delay equations

Evelyn Buckwar, Rachel Kuske, Salah-Eldin Mohammed, Tony Shardlow

Research output: Contribution to journalArticle

Abstract

We study weak convergence of an Euler scheme for nonlinear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
Original languageEnglish
Pages (from-to)60-99
Number of pages39
JournalLondon Mathematical Society Journal of Computation and Mathematics
Volume11
DOIs
Publication statusPublished - 7 May 2008

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