Overview
- The authors are the creators of this theory
- No competing book
- Interesting potential applications and further research
- Includes supplementary material: sn.pub/extras
Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 49)
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Table of contents (7 chapters)
Reviews
From the reviews:
"The book presents Tikhonov theorems for stochastic systems with two time scales when a parameter decreases to zero. … The topic of the book is relevant for the research areas of stochastics and of control and system theory. … The strength of the book is in the analysis of Tikhonov theorems … . The text is very well structured, runs very smooth, and the exposition allows detailed scrutiny of all proofs. The book is expected to become a basic reference on two-scale stochastic systems." (J. H. van Schuppen, Nieuw Archief voor Wiskunde, Vol. 6 (2), 2005)
"This research monograph needs to be placed on your shelves … . The monograph is organized by seven chapters and a valuable appendix. … The book is written for a graduated mathematically oriented readership who is supposed to be familiar with basic concepts of stochastic differential equations and related issues." (Henri Schurz, Zentralblatt MATH, Vol. 1033 (8), 2004)
"This very well-crafted monograph examines the coupled stochastic and singularly perturbed stochastic dynamics … . the monograph displays in a very attractive manner the general scene of singularly perturbed stochastic differential equations. Telling examples are provided along with enlightening explanations, comparisons and detailed background material needed to grasp the theory. … To sum up, a mixture of modern techniques concerning singularly perturbed stochastic differential equations, along with classical arguments, is presented in a rigorous, clear and attractive manner." (Zvi Artstein, Mathematical Reviews, 2004 c)
"Two time-scale problems arise in many problems of practical interest. The essential ingredient in these problems is a decomposition of the dynamics into ‘fast’ and ‘slow’ modes. … This book deals, inter alia with ‘averaging methods’ where the coefficients of the limiting slow dynamics are obtained by averaging the fast dynamics. Indeed, the idea of‘averaging’ has found wide-spread application in related problems. The book is uncompromisingly mathematical but clearly and elegantly written." (G. C. Goodwin, Short Book Reviews, Vol. 23 (3), 2003)
Authors and Affiliations
Bibliographic Information
Book Title: Two-Scale Stochastic Systems
Book Subtitle: Asymptotic Analysis and Control
Authors: Yuri Kabanov, Sergei Pergamenshchikov
Series Title: Stochastic Modelling and Applied Probability
DOI: https://doi.org/10.1007/978-3-662-13242-5
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Hardcover ISBN: 978-3-540-65332-5Published: 07 November 2002
Softcover ISBN: 978-3-642-08467-6Published: 05 December 2010
eBook ISBN: 978-3-662-13242-5Published: 17 April 2013
Series ISSN: 0172-4568
Series E-ISSN: 2197-439X
Edition Number: 1
Number of Pages: XIV, 266
Topics: Probability Theory and Stochastic Processes, Systems Theory, Control