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Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems
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Field name Details
Dewey Class 519.2
Title Random Perturbations of Dynamical Systems (EB) / by Mark I. Freidlin, Alexander D. Wentzell.
Author Freidlin, Mark Iosifovich , 1938-
Added Personal Name Wentzell, Alexander D.
Other name(s) SpringerLink (Online service)
Edition statement 3rd ed. 2012.
Publication Berlin, Heidelberg : Springer
, 2012.
Physical Details XXVIII, 458 pages, 48 illus. : online resource.
Series Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 260
ISBN 9783642258473
Note "The first edition of this book was published in 1979 in Russian"--Pref. to 2nd. ed.
Summary Note Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been ârediscoveredâ in applied papers.   In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained.   Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important.:
Contents note 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. The Multidimensional Case -- 10.Stability Under Random Perturbations -- 11.Sharpenings and Generalizations -- References -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-3-642-25847-3
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