This text is 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 stabilization, and asymptotics of stationary distributions are considered in detail. The author's 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 conncected with PDE. This second edition contains expansions on the averaging principle, a new chapter on random perturbations of Hamiltonian systems, along with results on fast oscillating perturbations of systems with conservations laws. New sections on wave front propagation in semilinear PDE and on random perturbations of certain infinite-dimensional dynamical systems have been incorporated into the chapter on sharpenings and generalizations.This text is a treatment of various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems.
|Title||:||Random Perturbations of Dynamical Systems|
|Author||:||Mark Iosifovich Freĭdlin, Alexander D. Wentzell|
|Publisher||:||Springer Science & Business Media - 1998-01-01|