Random Perturbations of Dynamical Systems

1. Front Matter

   Pages i-xi

   PDF

2. Introduction

   • M. I. Freidlin, A. D. Wentzell

   Pages 1-14

3. Random Perturbations

   • M. I. Freidlin, A. D. Wentzell

   Pages 15-43

4. Small Random Perturbations on a Finite Time Interval

   • M. I. Freidlin, A. D. Wentzell

   Pages 44-69

5. Action Functional

   • M. I. Freidlin, A. D. Wentzell

   Pages 70-102

6. Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point

   • M. I. Freidlin, A. D. Wentzell

   Pages 103-135

7. Perturbations Leading to Markov Processes

   • M. I. Freidlin, A. D. Wentzell

   Pages 136-160

8. Markov Perturbations on Large Time Intervals

   • M. I. Freidlin, A. D. Wentzell

   Pages 161-211

9. The Averaging Principle. Fluctuations in Dynamical Systems with Averaging

   • M. I. Freidlin, A. D. Wentzell

   Pages 212-282

10. Random Perturbations of Hamiltonian Systems

    • M. I. Freidlin, A. D. Wentzell

    Pages 283-360

11. Stability Under Random Perturbations

    • M. I. Freidlin, A. D. Wentzell

    Pages 361-376

12. Sharpenings and Generalizations

    • M. I. Freidlin, A. D. Wentzell

    Pages 377-416

13. Back Matter

    Pages 417-432

    PDF

The first edition of this book was published in 1979 in Russian. Most of the material presented was related to large-deviation theory for stochastic pro­ cesses. This theory was developed more or less at the same time by different authors in different countries. This book was the first monograph in which large-deviation theory for stochastic processes was presented. Since then a number of books specially dedicated to large-deviation theory have been pub­ lished, including S. R. S. Varadhan [4], A. D. Wentzell [9], J. -D. Deuschel and D. W. Stroock [1], A. Dembo and O. Zeitouni [1]. Just a few changes were made for this edition in the part where large deviations are treated. The most essential is the addition of two new sections in the last chapter. Large deviations for infinite-dimensional systems are briefly conside:red in one new section, and the applications of large-deviation theory to wave front prop­ agation for reaction-diffusion equations are considered in another one. Large-deviation theory is not the only class of limit theorems arising in the context of random perturbations of dynamical systems. We therefore included in the second edition a number of new results related to the aver­ aging principle. Random perturbations of classical dynamical systems under certain conditions lead to diffusion processes on graphs. Such problems are considered in the new Chapter 8.

• Boundary value problem
• Markov process
• Power
• dynamical systems
• stochastic processes

Second Edition

M.I. Freidlin; A.D. Wentzell; and J. Szücs

Random Perturbations of Dynamical Systems

"A very detailed and deep mathematical treatment of the long term behavior of randomly perturbed dynamical systems."—ZENTRALBLATT MATH

• Department of Mathematics, University of Maryland, College Park, USA

  M. I. Freidlin

• Department of Mathematics, Tulane University, New Orleans, USA

  A. D. Wentzell

Policies and ethics