Numerical Solutions of Neutral Stochastic Functional Differential Equations

This paper examines the numerical solutions of neutral stochastic functional differential equations ( NSFDEs) $d[x(t)\, - \,u(x_t )]\, = \,f(x_t )dt\, + \,g(x_t )dw(t),\,t \ge \,0$. The key contribution is to establish the strong mean square convergence theory of the Euler- Maruyama approximate solu...

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Vydáno v:SIAM journal on numerical analysis Ročník 46; číslo 4; s. 1821 - 1841
Hlavní autoři: Wu, Fuke, Mao, Xuerong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Témata:
Approximation
Brownian motion
Determinism
Differential equations
Integers
Lipschitz condition
Mathematical theorems
Numerical analysis
Perceptron convergence procedure
Random variables
Uniqueness
ISSN:0036-1429, 1095-7170
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Shrnutí:This paper examines the numerical solutions of neutral stochastic functional differential equations ( NSFDEs) $d[x(t)\, - \,u(x_t )]\, = \,f(x_t )dt\, + \,g(x_t )dw(t),\,t \ge \,0$. 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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/070697021