Random Perturbations Of Hamiltonian Systems

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Random Perturbations Of Hamiltonian Systems

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Author : Mark Iosifovich Freĭdlin
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Random Perturbations Of Hamiltonian Systems written by Mark Iosifovich Freĭdlin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

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.

Random Perturbations Of Hamiltonian Systems

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Author : Mark Iosifovich Freĭdlin
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-08-31

Random Perturbations Of Hamiltonian Systems written by Mark Iosifovich Freĭdlin and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with Diffusion processes categories.

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.

Random Perturbations Of Dynamical Systems

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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-31

Random Perturbations Of Dynamical Systems written by Mark I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-31 with Mathematics categories.

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.

Random Perturbations Of Dynamical Systems

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Author : Mark Iosifovich Freĭdlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Random Perturbations Of Dynamical Systems written by Mark Iosifovich Freĭdlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

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.

Random Perturbations Of Dynamical Systems

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Author : M. I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Random Perturbations Of Dynamical Systems written by M. I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

Chaos And Diffusion In Hamiltonian Systems

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Author :
language : en
Publisher: Atlantica Séguier Frontières
Release Date : 1995

Chaos And Diffusion In Hamiltonian Systems written by and has been published by Atlantica Séguier Frontières this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Chaotic behavior in systems categories.

On Random Perturbations Of Hamiltonian Systems With Many Degrees Of Freedom

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Author : Mark I. Frejdlin
language : en
Publisher:
Release Date : 2000

On Random Perturbations Of Hamiltonian Systems With Many Degrees Of Freedom written by Mark I. Frejdlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Topics In Stochastic Analysis And Nonparametric Estimation

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Author : Pao-Liu Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-19

Topics In Stochastic Analysis And Nonparametric Estimation written by Pao-Liu Chow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-19 with Mathematics categories.

This IMA Volume in Mathematics and its Applications TOPICS IN STOCHASTIC ANALYSIS AND NONPARAMETRIC ESTIMATION contains papers that were presented at the IMA Participating Institution conference on "Asymptotic Analysis in Stochastic Processes, Nonparamet ric Estimation, and Related Problems" held on September 15-17, 2006 at Wayne State University. The conference, which was one of approximately ten selected each year for partial support by the IMA through its affiliates program, was dedicated to Professor Rafail Z. Khasminskii on the occasion th of his 75 birthday, in recognition of his profound contributions to the field of stochastic processes and nonparametric estimation theory. We are grateful to the participants and, especially, to the conference organizers, for making the event so successful. Pao-Liu Chow, Boris Mor dukhovich, and George Yin of the Department of Mathematics at Wayne State University did a superb job organizing this first-rate event and in editing these proceedings. We take this opportunity to thank the Nation al Science Foundation for its support of the IMA.

Random Perturbations Of Dynamical Systems

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Author : Mark Freidlin
language : en
Publisher: Springer
Release Date : 2011-11-22

Random Perturbations Of Dynamical Systems written by Mark Freidlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-22 with Mathematics categories.

A treatment of various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems. Apart from the long-time behaviour of the perturbed system, exit problems, metastable states, optimal stabilisation, and asymptotics of stationary distributions are considered in detail. The authors'main tools are the large deviation theory, the central limit theorem for stochastic processes, and the averaging principle. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system, and most of these results are closely connected with PDEs. This new edition contains expansions on the averaging principle, a new chapter on random perturbations of Hamiltonian systems, along with new results on fast oscillating perturbations of systems with conservation laws. New sections on wave front propagation in semilinear PDEs and on random perturbations of certain infinite-dimensional dynamical systems have been incorporated into the chapter on sharpenings and generalisations.

Random Perturbation Methods With Applications In Science And Engineering

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Author : Anatoli V. Skorokhod
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-21

Random Perturbation Methods With Applications In Science And Engineering written by Anatoli V. Skorokhod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-21 with Mathematics categories.

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.