Random Perturbations of Dynamical Systems

✍ Scribed by M. I. Freidlin, A. D. Wentzell (auth.)

• Publisher: Springer-Verlag New York
• Year: 1984
• Tongue: English
• Leaves: 333
• Series: Grundlehren der mathematischen Wissenschaften 260
• Edition: 1
• Category: Library

✦ Synopsis

Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

✦ Table of Contents

Front Matter....Pages i-viii
Introduction....Pages 1-14
Random Perturbations....Pages 15-43
Small Random Perturbations on a Finite Time Interval....Pages 44-69
Action Functional....Pages 70-102
Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point....Pages 103-135
Perturbations Leading to Markov Processes....Pages 136-160
Markov Perturbations on Large Time Intervals....Pages 161-211
The Averaging Principle. Fluctuations in Dynamical Systems with Averaging....Pages 212-277
Stability Under Random Perturbations....Pages 278-293
Sharpenings and Generalizations....Pages 294-313
Back Matter....Pages 315-327

✦ Subjects

Analysis