Stochastic Modelling and Applied Probability

Stochastic Stability of Differential Equations

Authors: Khasminskii, Rafail

  • Completely revised and enlarged second edition
  • Important new results are contained
  • Useful for researchers and for students in graduate courses
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About this book

Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography.

This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.

Reviews

From the reviews of the second edition:

“Even more than 40 years after the publication of the first Russian edition, this monograph is still an excellent source for graduate students and researchers … . It is a great introduction to the subject of stochastic stability. Important concepts … are carefully explained, and many different types of stochastic stability are studied. … valuable reference for researchers -- not only researchers in mathematics, but in fact it should also be useful for engineers and physicists interested in stability of systems subject to random forcing.” (Nicolas Perkowski, Zentralblatt MATH, Vol. 1241, 2012)

“This is a comprehensive compendium of results on the stability of stochastic dynamical systems, being the second edition of the English translation of the original Russian work written by a researcher who has made a dominant contribution to the topic. … The bulk of the original text, however, is retained as such. … some of the material here is not often found in standard texts, and this book serves as a valuable source for it.” (Vivek S. Borkar, Mathematical Reviews, January, 2013)


Table of contents (8 chapters)

  • Boundedness in Probability and Stability of Stochastic Processes Defined by Differential Equations

    Khasminskii, Rafail

    Pages 1-42

  • Stationary and Periodic Solutions of Differential Equations

    Khasminskii, Rafail

    Pages 43-58

  • Markov Processes and Stochastic Differential Equations

    Khasminskii, Rafail

    Pages 59-98

  • Ergodic Properties of Solutions of Stochastic Equations

    Khasminskii, Rafail

    Pages 99-144

  • Stability of Stochastic Differential Equations

    Khasminskii, Rafail

    Pages 145-176

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-23280-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-23279-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-642-27028-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Stability of Differential Equations
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
66
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-23280-0
DOI
10.1007/978-3-642-23280-0
Hardcover ISBN
978-3-642-23279-4
Softcover ISBN
978-3-642-27028-4
Series ISSN
0172-4568
Edition Number
2
Number of Pages
XVIII, 342
Additional Information
Originally published in Russian, by Nauka, Moskow 1969. 1st English ed. published 1980 under R.Z. Has'minski in the series Mechanics: Analysis by Sijthoff & Noordhoff.
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