Alexander D. Wentzell's Books

Random Perturbations of Dynamical Systems

By: Mark I. Freidlin,Alexander D. Wentzell

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Random Perturbations of Dynamical Systems

By: Mark I. Freidlin,Alexander D. Wentzell

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 “rediscovered” 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.

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483

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Springer Science & Business Media

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ISBN 10

3642258476

ISBN 13

9783642258473

Random Perturbations of Dynamical Systems

By: Mark Iosifovich Freĭdlin,Alexander D. Wentzell

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Random Perturbations of Dynamical Systems

By: Mark Iosifovich Freĭdlin,Alexander D. Wentzell

The authors' main tools are the large deviation theory the centred limit theorem for stochastic processes, and the averaging principle - all presented in great detail. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system.

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448

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Springer Science & Business Media

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ISBN 10

0387983627

ISBN 13

9780387983622

Random Perturbations of Hamiltonian Systems

By: Mark Iosifovich Freĭdlin,Alexander D. Wentzell

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Random Perturbations of Hamiltonian Systems

By: Mark Iosifovich Freĭdlin,Alexander D. Wentzell

Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

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American Mathematical Soc.

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ISBN 10

0821825860

ISBN 13

9780821825860

Book's by Alexander D. Wentzell

Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems

Random Perturbations of Dynamical Systems

Random Perturbations of Hamiltonian Systems

Random Perturbations of Hamiltonian Systems

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