An approximate method via Taylor series for stochastic functional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:363

Article

Milosevic, Marija¹  Jovanovic, Miljana¹  Jankovic, Svetlana¹ 

[1] Univ Nis, Fac Sci & Math, Nish 18000, Serbia

关键词: Stochastic functional differential equation;    Frechet derivative;    Taylor approximation;    L-p and almost sure convergence;   

DOI  :  10.1016/j.jmaa.2009.07.061

来源: Elsevier

【 摘 要 】

The subject of this paper is an analytic approximate method for stochastic functional differential equations whose coefficients are functionals, sufficiently smooth in the sense of Frechet derivatives. The approximate equations are defined on equidistant partitions of the time interval, and their coefficients are general Taylor expansions of the coefficients of the initial equation. It will be shown that the approximate solutions converge in the L-p-norm and with probability one to the solution of the initial equation, and also that the rate of convergence increases when degrees in Taylor expansions increase, analogously to real analysis. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free