Random Perturbations of Dynamical Systems
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Beschreibung
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.
***preliminary version*** This volume is concerned with a different kind of limit theorem for stochastic processes defined as a result of random perturbations of dynamical systems; and in particular with the long-time behavior of the perturbed system. The most essential additions and changes in this new edition concern the averaging principle. A new chapter on random perturbations of Hamiltonian systems has been added along with new results on fast oscillating perturbations of systems with conservation laws.
Autor*in
Mark I. Freidlin
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Second EditionM.I. Freidlin; A.D. Wentzell; and J. SzücsRandom Perturbations of Dynamical Systems"A very detailed and deep mathematical treatment of the long term behavior of randomly perturbed dynamical systems."—ZENTRALBLATT MATH
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