Stochastic Stability of Differential Equations

✍ Scribed by Rafail Khasminskii (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2012
• Tongue: English
• Leaves: 358
• Series: Stochastic Modelling and Applied Probability 66
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XVII
Boundedness in Probability and Stability of Stochastic Processes Defined by Differential Equations....Pages 1-42
Stationary and Periodic Solutions of Differential Equations....Pages 43-58
Markov Processes and Stochastic Differential Equations....Pages 59-98
Ergodic Properties of Solutions of Stochastic Equations....Pages 99-144
Stability of Stochastic Differential Equations....Pages 145-176
Systems of Linear Stochastic Equations....Pages 177-226
Some Special Problems in the Theory of Stability of SDE’s....Pages 227-251
Stabilization of Controlled Stochastic Systems....Pages 253-263
Back Matter....Pages 265-339

✦ Subjects

Probability Theory and Stochastic Processes;Mechanics