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Numerical solutions of neutral stochastic functional differential equations

WU, F. and Mao, X. and , Chinese Scholarship Council (Funder) (2008) Numerical solutions of neutral stochastic functional differential equations. SIAM Journal on Numerical Analysis, 46 (4). pp. 1821-1841. ISSN 0036-1429

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Abstract

This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) $d[x(t)-u(x_t)]=f(x_t)dt+g(x_t)dw(t)$, $t\geq 0$. The key contribution is to establish the strong mean square convergence theory of the Euler-Maruyama approximate solution under the local Lipschitz condition, the linear growth condition, and contractive mapping. These conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here are obtained under quite general conditions. Although the way of analysis borrows from [X. Mao, LMS J. Comput. Math., 6 (2003), pp. 141-161], to cope with $u(x_t)$, several new techniques have been developed.

Item type: Article
ID code: 13830
Keywords: neutral stochastic functional differential equations, strong convergence, Euler-Maruyama method, local Lipschitz condition, Mathematics, Numerical Analysis
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Mrs Carolynne Westwood
Date Deposited: 17 Dec 2009 16:29
Last modified: 23 Jul 2015 22:11
URI: http://strathprints.strath.ac.uk/id/eprint/13830

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