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Random Perturbations of Dynamical Systems (Grundlehren der mathematischen Wissenschaften)
Rok: 1984
ISBN: 9780387908588
OKCZID: 110389312
Citace (dle ČSN ISO 690):
FREIDLIN, M. I. Random perturbations of dynamical systems. Překlad Joseph SZÜCS. New York, N.Y.: Springer-Verlag, c1984. viii, 326 s. Grundlehren der mathematischen Wissenschaften, v. 260.
Anotace
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.