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" Two-Scale Stochastic Systems : "
by Yuri Kabanov, Sergei Pergamenshchikov.
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BL
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| Record Number
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760923
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b580896
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| Main Entry
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by Yuri Kabanov, Sergei Pergamenshchikov.
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| Title & Author
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Two-Scale Stochastic Systems : : Asymptotic Analysis and Control\ by Yuri Kabanov, Sergei Pergamenshchikov.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
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| Series Statement
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Applications of Mathematics, Stochastic Modelling and Applied Probability, 49.
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(xiv, 266 pages)
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| ISBN
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3662132427
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: 9783662132425
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| Contents
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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 --; Appendix.
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| Abstract
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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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Distribution (Probability theory)
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Mathematics.
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Systems theory.
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| LC Classification
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QA402.37B998 2003
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| Added Entry
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Sergei Pergamenshchikov
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Yuri Kabanov
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