Anatoli V. Skorokhod, Frank C. Hoppensteadt, Habib Salehi (eds.)9780387224466, 9780387954271, 0387954279
As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLAB-based computer simulations.
This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems. |
Table of contents :
Front Matter….Pages i-xi
Introduction….Pages 1-48
Ergodic Theorems….Pages 49-63
Convergence Properties of Stochastic Processes….Pages 64-87
Averaging….Pages 88-113
Normal Deviations….Pages 114-132
Diffusion Approximation….Pages 133-171
Stability….Pages 172-231
Markov Chains with Random Transition Probabilities….Pages 232-256
Randomly Perturbed Mechanical Systems….Pages 257-302
Dynamical Systems on a Torus….Pages 303-342
Phase-Locked Loops….Pages 343-375
Models in Population Biology….Pages 376-423
Genetics….Pages 424-451
Back Matter….Pages 452-490 |
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