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Weak approximation of stochastic differential delay equations for bounded measurable function

Part of: Functional-differential and differential-difference equations Stochastic analysis

Published online by Cambridge University Press:  01 September 2013

Hua Zhang
Hua Zhang*
Affiliation:
School of Statistics,Jiangxi University of Finance and Economics,Nanchang, Jiangxi 330013, PR China email zh860801@163.com School of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou, Guangdong 510275, PR China email zh860801@163.com

Abstract

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In this paper we study the weak approximation problem of $E[\phi (x(T))] $ by $E[\phi (y(T))] $, where $x(T)$ is the solution of a stochastic differential delay equation and $y(T)$ is defined by the Euler scheme. For $\phi \in { C}_{b}^{3} $, Buckwar, Kuske, Mohammed and Shardlow (‘Weak convergence of the Euler scheme for stochastic differential delay equations’, LMS J. Comput. Math. 11 (2008) 60–69) have shown that the Euler scheme has weak order of convergence $1$. Here we prove that the same results hold when $\phi $ is only assumed to be measurable and bounded under an additional non-degeneracy condition.

MSC classification

Secondary: 34K50: Stochastic functional-differential equations 60H07: Stochastic calculus of variations and the Malliavin calculus 60H35: Computational methods for stochastic equations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 319 - 343
Copyright
© The Author(s) 2013 

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