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Semi-Markov Random Evolutions : Mathematics and Its Applications - Vladimir S. Koroliuk

Semi-Markov Random Evolutions

Mathematics and Its Applications

Hardcover Published: November 1994
ISBN: 9780792331506
Number Of Pages: 310

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The evolution of systems is a growing field of interest stimulated by many possible applications. This book is devoted to semi-Markov random evolutions (SMRE). This class of evolutions is rich enough to describe the evolutionary systems changing their characteristics under the influence of random factors. At the same time there exist efficient mathematical tools for investigating the SMRE. The topics addressed in this book include classification, fundamental properties of the SMRE, averaging theorems, diffusion approximation and normal deviations theorems for SMRE in ergodic case and in the scheme of asymptotic phase lumping. Both analytic and stochastic methods for investigation of the limiting behaviour of SMRE are developed. This book includes many applications of rapidly changing semi-Markov random media, including storage and traffic processes, branching and switching processes, stochastic differential equations, motions on Lie groups, and harmonic oscillations. This volume will be of interest to statisticians whose work involves operator theory, functional analysis, systems theory and cybernetics.

Preface
Introductionp. 1
Markov Renewal Processesp. 7
Phase Merging of Semi-Markov Processesp. 27
Semi-Markov Random Evolutionsp. 59
Algorithms of Phase Averaging for Semi-Markov Random Evolutionsp. 93
Compactness of Semi-Markov Random Evolutions in the Averaging Schemep. 117
Limiting Representations for Semi-Markov Random Evolutions in the Averaging Schemep. 145
Compactness of Semi-Markov Random Evolutions in the Diffusion Approximationp. 175
Stochastic Integral Limiting Representations of Semi-Markov Random Evolutions in the Diffusion Approximationp. 207
Application of the Limit Theorems to Semi-Markov Random Evolutions in the Averaging Schemep. 237
Application of the Diffusion Approximation of Semi-Markov Random Evolutions to Stochastic Systems in Random Mediap. 265
Double Approximation of Random Evolutionsp. 277
Referencesp. 289
Subject Indexp. 305
Notationp. 309
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792331506
ISBN-10: 0792331508
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 310
Published: November 1994
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.63

Earn 519 Qantas Points
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