Research Catalog

Title

Random perturbations of dynamical systems / M.I. Freidlin, A.D. Wentzell ; translated by Joseph Szücs.

Author

Freĭdlin, M. I. (Mark Iosifovich)

Publication

New York : Springer-Verlag, ©1984.

Items in the Library & Off-site

Details

Additional Authors

• Wentzell, Alexander D.
• Szücs, Joseph

Description

viii, 326 pages : illustrations; 25 cm

Summary

Asymptotic 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 play a 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.

Series Statement

Grundlehren der mathematischen Wissenschaften ; 260

Uniform Title

• Fluktuat︠s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ. English
• Grundlehren der mathematischen Wissenschaften ; 260.

Alternative Title

Fluktuat︠s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ.

Subject

• Markov processes
• Gaussian processes
• Stochastic processes
• Perturbation (Mathematics)
• Markov Chains
• Stochastic Processes
• 31.70 probability
• 33.11 classical mechanics
• Dynamische systemen
• Stochastische processen
• STOCHASTIC PROCESSES
• PERTURBATION THEORY
• Systèmes dynamiques
• Probabilités
• Perturbation (astronomie)
• Perturbation (mathématiques)
• Processus stochastiques

Note

• Translation of: Fluktuat︠s︡ii v dinamicheskikh sistemakh pod deĭstviem malykh sluchaĭnykh vozmushcheniĭ / A.D. Ventt︠s︡elʹ. 1979.
• Includes index.

Bibliography (note)

• Bibliography: p. [315]-323.

Contents

Introduction -- Random perturbations -- Small random perturbations on a finite time interval -- Action functional -- Gaussian perturbations of dynamical systems ; Neighborhood of an equilibrium point -- Perturbations leading to Markov processes -- Markov perturbations on large time intervals -- The averaging principle ; Fluctuations in dynamical systems with averaging -- Stability under random perturbations -- Sharpenings and generalizations.

ISBN

• 0387908587
• 9780387908588
• 3540908587
• 9783540908586

LCCN

83004712

OCLC

• ocm09413365
• 9413365
• SCSB-85705

Owning Institutions

Princeton University Library