Evolution of Systems in Random Media: 1st Edition (Hardback) book cover

Evolution of Systems in Random Media

1st Edition

By Vladimir S. Korolyuk, Anatoly V. Swishchuk

CRC Press

368 pages

Purchasing Options:$ = USD
Hardback: 9780849394058
pub: 1995-09-11
$265.00
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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

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis