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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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书目名称Random Perturbations of Dynamical Systems
编辑M. I. Freidlin,A. D. Wentzell
视频video
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Random Perturbations of Dynamical Systems;  M. I. Freidlin,A. D. Wentzell Book 19841st edition Springer-Verlag New York Inc. 1984 Dynamisch
描述Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. 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.
出版日期Book 19841st edition
关键词Dynamisches System; Perturbation; Stochastischer Prozess; Störung (Math; ); Systems; dynamical systems
版次1
doihttps://doi.org/10.1007/978-1-4684-0176-9
isbn_ebook978-1-4684-0176-9Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag New York Inc. 1984
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Action Functional,We consider a random process . in the space . defined by the stochastic differential equation
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https://doi.org/10.1007/978-1-4684-0176-9Dynamisches System; Perturbation; Stochastischer Prozess; Störung (Math; ); Systems; dynamical systems
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Markov Perturbations on Large Time Intervals, Theorem 3.2 of Ch. 5 and the behavior of probabilities of large deviations from the “most probable” trajectory—the trajectory of the dynamical system . —can be described as ε → 0, by the action functional .where
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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.
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