Titlebook: Random Perturbations of Dynamical Systems; Mark I. Freidlin,Alexander D. Wentzell Textbook 2012Latest edition Springer-Verlag Berlin Heide

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The Averaging Principle. Fluctuations in Dynamical Systems with Averaging,In Chap. 7, rapidly oscillating stochastic perturbations of dynamical systems are considered. Results of the law-of-large-numbers type, those of central-limit theorem type, and large-deviation results are obtained. Those last results are applied to the asymptotics of the behavior of the perturbed dynamical system on growing time intervals.

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Mark I. Freidlin,Alexander D. WentzellThird revised and enlarged edition.New chapters and enlarged bibliographic references.A very detailed and deep mathematical treatment of the long term behavior of randomly perturbed dynamical systems.

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Sharpenings and Generalizations,ation results of Chaps. 3–5 to wave propagation in semi-linear partial differential equations (in the spirit of the Kolmogorov–Petrovskii–Piskunov problem for reaction-diffusion equations); and large deviations for infinite-dimensional systems described by stochastic partial differential equations.

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The Multidimensional Case,low motion. If the non-perturbed system has no saddle-type points, we can, in the one-degree-of-freedom case, characterize the slow motion by the value of the Hamiltonian (in the multidimensional case with several first integrals, by the values of those first integrals). If there are saddle-type poi

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0072-7830 ain 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 deterministi978-3-642-44687-0978-3-642-25847-3Series ISSN 0072-7830 Series E-ISSN 2196-9701

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