Semi-Markov Random Evolutions

  • V. Korolyuk
  • A. Swishchuk

Part of the Mathematics and Its Applications book series (MAIA, volume 308)

Table of contents

  1. Front Matter
    Pages i-x
  2. V. Korolyuk, A. Swishchuk
    Pages 1-6
  3. V. Korolyuk, A. Swishchuk
    Pages 7-26
  4. V. Korolyuk, A. Swishchuk
    Pages 27-58
  5. V. Korolyuk, A. Swishchuk
    Pages 59-91
  6. V. Korolyuk, A. Swishchuk
    Pages 277-288
  7. Back Matter
    Pages 289-310

About this book

Introduction

The evolution of systems in random media is a broad and fruitful field for the applica­ tions of different mathematical methods and theories. This evolution can be character­ ized by a semigroup property. In the abstract form, this property is given by a semigroup of operators in a normed vector (Banach) space. In the practically boundless variety of mathematical models of the evolutionary systems, we have chosen the semi-Markov ran­ dom evolutions as an object of our consideration. The definition of the evolutions of this type is based on rather simple initial assumptions. The random medium is described by the Markov renewal processes or by the semi­ Markov processes. The local characteristics of the system depend on the state of the ran­ dom medium. At the same time, the evolution of the system does not affect the medium. Hence, the semi-Markov random evolutions are described by two processes, namely, by the switching Markov renewal process, which describes the changes of the state of the external random medium, and by the switched process, i.e., by the semigroup of oper­ ators describing the evolution of the system in the semi-Markov random medium.

Keywords

Markov process Markov renewal process Operator theory algorithm algorithms classification functional analysis stochastic differential equation stochastic systems systems theory

Authors and affiliations

  • V. Korolyuk
    • 1
  • A. Swishchuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-1010-5
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-4439-4
  • Online ISBN 978-94-011-1010-5
  • About this book
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