1st Edition

Evolution of Systems in Random Media



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ISBN 9780849394058
Published September 11, 1995 by CRC Press
368 Pages

USD $84.95

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Book Description

Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.

Table of Contents

Introduction
The Martingale Problem and Weak Convergence in Banach Space
Random Processes and Martingales in Banach Space
Operator Semi-Groups
Markov Processes: Martingale Characterization
Weak Convergence
Martingale Problem in Banach Space
Markov Renewal Processes
Semi-Markov Processes
Singular Perturbed Problems
Perturbation of Reducible-Invertible Operators
Phase Merging of Semi-Markov Processes
Semi-Markov Random Evolutions
Definition and Classification of Random Evolutions
Stochastic Models of Systems
Inhomogeneous Semi-Markov Random Evolutions
Weak Convergence of Random Evolutions
Relative Compactness of Random Evolutions
Limiting Evolutions in Averaging and Diffusion Approximation Schemes
Uniqueness of the Solution of the Martingale Problem
Averaging and Diffusion Approximation of Random Evolution in Reducible Random Media
Averaging of Stochastic Systems in Semi-Markov Random Media
Compacts in Banach Spaces
Traffic Processes
Impulse Traffic Processes
Additive Functionals
Stochastic Differential Equations
U-Statistical Processes
Random Evolutions on Lie Groups
Oscillations of a Harmonic Oscillator
Waves in Conductors and Beams
Diffusion Approximation of Stochastic Systems
Traffic Processes
Impulse Traffic Processes
Additive Functionals
U-Statistical Processes
Random Motions on Lie Groups
Normal Deviations of Semi-Markov Random Evolutions
Random Evolution in Ergodic Media
Stochastic Systems
Random Evolution in Reducible Media
Evolutionary Stochastic Systems in Reducible Media
Rates of Convergence in the Limit Theorems for Random Evolutions
Averaging Schemes for Random Evolutions
Diffusion Approximation Scheme for Random Evolutions
Averaging Scheme for Evolutionary Stochastic Systems in Random Media
Diffusion Approximation Scheme for Evolutionary Stochastic Systems in Random Media
Stability of Stochastic Systems
Traffic Process in the Averaging Scheme
Traffic Process in the Diffusion Approximation Scheme
Impulse Traffic Process in the Averaging Scheme
Impulse Traffic Process in the Diffusion Approximation Scheme
Control of Evolutionary Stochastic Systems in Random Media
Functionals of Uncontrolled Processes
Cost Functionals
Optimal Stochastic Control
Bibliography
Subject Index

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