عنوان

Two-Scale Stochastic Systems :

(Number (ISBN

3662132427

(Number (ISBN

9783662132425

Number

b580896

Title Proper

Two-Scale Stochastic Systems :

General Material Designation

[Book]

Other Title Information

Asymptotic Analysis and Control

First Statement of Responsibility

by Yuri Kabanov, Sergei Pergamenshchikov.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

2003

Specific Material Designation and Extent of Item

(xiv, 266 pages)

Series Title

Applications of Mathematics, Stochastic Modelling and Applied Probability, 49.

Text of Note

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.

Text of Note

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.

Distribution (Probability theory)

Mathematics.

Systems theory.

Class number

Book number

by Yuri Kabanov, Sergei Pergamenshchikov.

Sergei Pergamenshchikov

Yuri Kabanov

Electronic name

[Book]

Y