Volume 8, Issue 2
Mean Square Convergence of Stochastic Theta-methods for Nonlinear Neutral Stochastic Differential Delay Equations

S. Gan, H. Schurz & H. Zhang

DOI:

Int. J. Numer. Anal. Mod., 8 (2011), pp. 201-213

Published online: 2011-08

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  • Abstract

This paper is devoted to the convergence analysis of stochastic theta-methods for nonlinear neutral stochastic differential delay equations (NSDDEs) in Ito sense. The basic idea is to reformulate the original problem eliminating the dependence on the differentiation of the solution in the past values, which leads to a stochastic differential algebraic system. Drift-implicit stochastic theta-methods are proposed for the coupled system. It is shown that the stochastic theta-methods are mean-square convergent with order 1/2 for Lipschitz continuous coefficients of underlying NSDDEs. A nonlinear numerical example illustrates the theoretical results.

  • Keywords

neutral stochastic differential delay equations mean-square continuity stochastic theta-methods mean-square convergence consistency

  • AMS Subject Headings

65C30 60H10 60H35 65C20

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COPYRIGHT: © Global Science Press

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