Author | Freidlin, M. I. author |
---|---|

Title | Random Perturbations of Dynamical Systems [electronic resource] / by M. I. Freidlin, A. D. Wentzell |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |

Edition | Second Edition |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0611-8 |

Descript | XI, 432 p. online resource |

SUMMARY

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 proยญ 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 pubยญ 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 propยญ 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 averยญ 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

CONTENT

1 Random Perturbations -- 2 Small Random Perturbations on a Finite Time Interval -- 3 Action Functional -- 4 Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point -- 5 Perturbations Leading to Markov Processes -- 6 Markov Perturbations on Large Time Intervals -- 7 The Averaging Principle. Fluctuations in Dynamical Systems with Averaging -- 8 Random Perturbations of Hamiltonian Systems -- 9 Stability Under Random Perturbations -- 10 Sharpenings and Generalizations -- References

Mathematics
Probabilities
Mathematics
Probability Theory and Stochastic Processes