Asymptotic expansions of solutions of integro-differential equations for transition densities of singularly perturbed switching diffusions: Rapid switchings

被引：30

作者：

Il'in, AM ^{[1
]}

Khasminskii, RZ

Yin, G

机构：

[1] Russian Acad, Inst Math & Mech, Ural Branch, Ekaterinburg, Russia

[2] Wright State Univ, Dept Math, Detroit, MI USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1999年 / 238卷 / 02期

基金：

美国国家科学基金会;

关键词：

forward equation; singular perturbation; asymptotic expansion;

D O I：

10.1006/jmaa.1998.6532

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work develops asymptotic expansions for solutions of integro-differential equations arising from transition densities of singularly perturbed switching-diffusion processes. The underlying processes have two components, namely the switching component and the diffusion component. Processes with rapid switchings are examined here. Under suitable conditions, it is proved that the asymptotic expansion is uniformly valid in the domain of interest. (C) 1999 Academic Press.

引用

页码：516 / 539

页数：24

共 23 条

[1]

[Anonymous], 1968, ANN SCUOLA NORM-SCI

[2]

[Anonymous], T MATH MONOGRAPHS

[3]

Bogoliubov NN., 1961, ASYMPTOTIC METHODS T

[4]

Eidelman S.D., 1969, PARABOLIC SYSTEMS, P469

[5]

FRIEDMAN A, 1967, PARTIAL DIFFERENTIAL

[6]

Gihman Iosif, 1979, THEORY STOCHASTIC PR, VIII

[7]

Hutson V., 2005, Applications of functional analysis and operator theory

[8]

Ikeda N., 1989, STOCHASTIC DIFFERENT, DOI DOI 10.1002/BIMJ.4710320720

[9]

ILIN AM, IN PRESS J OPTIM THE

[10]

Khas'minskii R. Z., 1968, Kybernetika, V4, P260

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