Two-Scale Stochastic Systems

Asymptotic Analysis and Control

Yuri Kabanov, Sergei Pergamenshchikov

280 pages, parution le 20/11/2002

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Résumé

Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behavior of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Contents

Warm-up
Toolbox: moment bounds for solutions of stable SDEs
The Tikhonov theory for SDEs
Large deviations
Uniform expansions for two-scale systems
Two-scale optimal control problems
Applications

L'auteur - Yuri Kabanov

Universite de Besancon, France

L'auteur - Sergei Pergamenshchikov

Universite de Rouen, France

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Yuri Kabanov, Sergei Pergamenshchikov
Parution	20/11/2002
Nb. de pages	280
Format	16 x 24
Couverture	Relié
Poids	537g
Intérieur	Noir et Blanc
EAN13	9783540653325