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Stochastic Stability of Differential Equations

  • Book
  • © 2012
  • Latest edition


  • Completely revised and enlarged second edition

  • Important new results are contained

  • Useful for researchers and for students in graduate courses

  • Includes supplementary material:

Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 66)

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Table of contents (8 chapters)


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.


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)

Authors and Affiliations

  • Mathematics Department, 1150 Faculty/Administration Building, Wayne State University, Detroit, USA

    Rafail Khasminskii

Bibliographic Information

  • Book Title: Stochastic Stability of Differential Equations

  • Authors: Rafail Khasminskii

  • Series Title: Stochastic Modelling and Applied Probability

  • DOI:

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Hardcover ISBN: 978-3-642-23279-4Published: 21 September 2011

  • Softcover ISBN: 978-3-642-27028-4Published: 27 November 2013

  • eBook ISBN: 978-3-642-23280-0Published: 20 September 2011

  • Series ISSN: 0172-4568

  • Series E-ISSN: 2197-439X

  • 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.

  • Topics: Probability Theory and Stochastic Processes, Classical Mechanics

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