On averaging principles: An asymptotic expansion approach

被引：86

作者：

Khasminskii, RZ ^{[1
]}

Yin, G ^{[1
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2004年 / 35卷 / 06期

关键词：

singular perturbation; diffusion; Kolmogorov backward equation; asymptotic expansion;

D O I：

10.1137/S0036141002403973

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is concerned with diffusion processes having fast and slow components. It was known that under suitable assumptions the slow component can be approximated by the Markov process with averaged characteristics. In this work, asymptotic expansions for the solutions of the Kolmogorov backward equations are constructed and justified. Certain probabilistic conclusions and examples are also provided.

引用

页码：1534 / 1560

页数：27

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