Titlebook: Random Perturbations of Dynamical Systems; M. I. Freidlin,A. D. Wentzell Book 19841st edition Springer-Verlag New York Inc. 1984 Dynamisch

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Sharpenings and Generalizations,e arises the following question: Is it possible to obtain subtler results for families of random processes (similar to those obtained for sums of independent random variables)—local limit theorems on large deviations and theorems on sharp asymptotics? There is some work in this direction; we give a survey of the results in this section.

LAIR

Springer-Verlag New York Inc. 1984

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Random Perturbations of Dynamical Systems978-1-4684-0176-9Series ISSN 0072-7830 Series E-ISSN 2196-9701

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Book 19841st edition. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

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Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point,tated, we shall assume that the functions . are bounded and satisfy a Lipschitz condition: |.(.) - .(.)| ≤ .|. - .|, |.(.)| ≤ . < ∞. Here we pay particular attention to the case where the perturbed process has the form.where . is an .-dimensional Wiener process.

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Perturbations Leading to Markov Processes, viewed as generalizations of the scheme of summing independent random variables; the constructions used in the study of large deviations for Markov processes generalize constructions encountered in the study of sums of independent terms.

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Stability Under Random Perturbations,e initial conditions or of the right side of an equation. In this chapter we consider some problems concerning stability under random perturbations. First we recall the basic notions of classical stability theory. Let the dynamical system.in .. have an equilibrium position at the point .:.) = 0.