Random perturbations of dynamical systems
著者
書誌事項
Random perturbations of dynamical systems
（Die Grundlehren der mathematischen Wissenschaften, 260）
Springer, 1998
2nd ed
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注記
"[Based on the] original Russian edition: Fluktuat︠s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ, Nauka : Moscow, 1979"--T.p. verso
Includes bibliographical references (p. [417]-427) and index
内容説明・目次
内容説明
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.
目次
1: Random Perturbations. 2: Small Random Perturbations on a Finite Time Interval. 3: Action Functional. 4: Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point. 5: Perturbations Leading to Markov Processes. 6: Markov Perturbations on Large Time Intervals. 7: The Averaging Principle. Fluctuations in Dynamical Systems with Averaging. 8: Random Perturbations of Hamiltonian Systems. 9: Stability Under Random Perturbations. 10: Sharpenings and Generalizations.
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