Numerical solutions of neutral stochastic functional differential equations

Fuke Wu, Xuerong Mao, Chinese Scholarship Council (Funder)

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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.
Original languageEnglish
Pages (from-to)1821-1841
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number4
DOIs
Publication statusPublished - 16 Apr 2008

Keywords

  • neutral stochastic functional differential equations
  • strong convergence
  • Euler-Maruyama method
  • local Lipschitz condition

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