The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus

被引：40

作者：

Kloeden, P. E. ^{[1
]}

Shardlow, T. ^{[2
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60325 Frankfurt, Germany

[2] Univ Manchester, Sch Math, Manchester, Lancs, England

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2012年 / 30卷 / 02期

关键词：

Delay equations; Milstein method; SDDE; Stochastic differential equations; Strong convergence; Taylor expansions;

D O I：

10.1080/07362994.2012.628907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This article employs an elementary method to derive the Milstein scheme and its first order strong rate of convergence for stochastic delay differential equations.

引用

页码：181 / 202

页数：22

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