Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften)

出版者:Springer

作者:Mark I. Freidlin

页数:459

出版时间:1998-10-23

价格:USD 139.00

装帧:Hardcover

isbn号码:9780387983622

丛书系列:Grundlehren der mathematischen Wissenschaften

图书标签:概率专著

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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.