Random Perturbation Methods with Applications in Science and Engineering

By: Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib D. Salehi

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Hardcover | 9 July 2002

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508 Pages

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24.77 x 16.51 x 2.54

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This book covers the impact of noise on models that are widely used in science and engineering applications. It applies perturbed methods which assume noise changes on a faster time or space scale than the system being studied. The book is written in two parts. The first part presents a careful development of mathematical methods needed to study random perturbations of dynamical systems. The second part presents non-random problems in a variety of important applications. Such problems are reformulated to account for both external and system random noise. Finally, the results from Part I are applied to analyze, simulate, and visualize the same problems now perturbed by noise. Applications from mechanical, electrical, and biological problems are discussed. In addition, numerous computer simulations and examples are included. Researchers and graduate students in mathematics and engineering will find this book useful.

Industry Reviews

From the reviews:

"The authors introduce the reader to the mathematical theory of randomly perturbed dynamical systems. ... the authors make the laudable attempt to introduce others, e.g. engineers and biologists (and non-expert mathematicians) ... by starting the book with an Introduction that in less technical terms illustrates the main facts of the theory and how these facts help one better understand the dynamical systems considered by scientists and engineers. This, together with many computer-simulated visualizations, may make the book accessible to scientists and engineers ... ." (Volker Wihstutz, Mathematical Reviews, 2003 m)

"This monograph contains a well-written rigorous mathematical treatment ... and deals with modern concepts such as dynamical systems, stochastic processes, stability, Markov chains, population biology, etc. ... In summary, this reviewer would definitely recommend Random Perturbation Methods with Applications in Science and Engineering to those researchers and graduate students ... who require tools to investigate stochastic systems. The book qualifies to be a reference work that certainly would be a valuable addition in libraries of universities and laboratories pursuing research in Applied Mathematics." (VD Radulescu, Applied Mechanics Reviews, Vol. 56 (4), 2003)

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Preface
Introduction	p. 1
Ergodic Theorems	p. 49
Convergence Properties of Stochastic Processes	p. 64
Averaging	p. 88
Normal Deviations	p. 114
Diffusion Approximation	p. 133
Stability	p. 172
Markov Chains with Random Transition Probabilities	p. 232
Randomly Perturbed Mechanical Systems	p. 257
Dynamical Systems on a Torus	p. 303
Phase-Locked Loops	p. 343
Models in Population Biology	p. 376
Genetics	p. 424
A: Some Notions of Probability Theory	p. 452
B: Commentary	p. 469
References	p. 472
Index	p. 485
Table of Contents provided by Blackwell. All Rights Reserved.

Random Perturbation Methods with Applications in Science and Engineering

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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