Mark I. Freidlin, Alexander D. Wentzell

eBook, PDF

Random Perturbations of Dynamical Systems (eBook, PDF)

Beschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 432
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461206118
• Artikelnr.: 43992500

Rezensionen

From the reviews of the third edition:

"The celebrated work of Ventsel and Freidlin has proved to be a major contribution in this development, with their phenomenal text Random Perturbations of Dynamical Systems, now in its third edition, playing a unique role. ... The book under review has evolved since its first English edition was published in 1984, a translation from the Russian original of 1979. ... it will attract an ever growing population of applied mathematicians to the fascinating new frontier of stochastic dynamics." (Hong Qian and Hao Ge, SIAM Review, Vol. 55 (3), 2013)