Two-Scale Stochastic Systems
Subtitle: Asymptotic Analysis and Control
By: by Yuri Kabanov, Sergei Pergamenshchikov
Contributors: Pergamenshchikov, Sergei
Series: Applications of Mathematics, Stochastic Modelling and Applied Probability -- 49; Applications of Mathematics, Stochastic Modelling and Applied Probability -- 49
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 266
ISBN-13: 9783642084676; 9783662132425
Subjects: Mathematics; Distribution (Probability theory); Systems theory
Description: 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 behaviour 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.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 behaviour 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.
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Table of contents: title: Warm-up; title: Toolbox: moment bounds for solutions of stable SDEs; title: The Tikhonov theory for SDEs; title: Large deviations; title: Uniform expansions for two-scale systems; title: Two-scale optimal control problems; title: Applications; title: Appendix.