Vladimir V. Korolyuk's Books

Stochastic Models of Systems

By: Vladimir S. Korolyuk,Vladimir V. Korolyuk

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Stochastic Models of Systems

By: Vladimir S. Korolyuk,Vladimir V. Korolyuk

In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics.

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Page Count

195

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940114625X

ISBN 13

9789401146258

Semi-Markov Random Evolutions

By: Vladimir S. Korolyuk,Anatoly Swishchuk

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Semi-Markov Random Evolutions

By: Vladimir S. Korolyuk,Anatoly Swishchuk

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.

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Page Count

315

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401110107

ISBN 13

9789401110105

Topics on Regenerative Processes

By: Vladimir V. Kalashnikov

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Topics on Regenerative Processes

By: Vladimir V. Kalashnikov

Regenerative processes are a popular subject in pure and applied probability, as well as in engineering (particularly simulation). This book provides important insight into new methods for investigating regenerative processes. Quantitative estimates play the key role in the book, and all developed methods support possibilities for obtaining such estimates, including probability metrics, test functions, crossing, and coupling. These methods are applied to a variety of problems, such as Markov chains, simulation, queueing systems, storage, and reliability. The book illustrates a unique application of the theory of probability metrics for examining regenerative processes, and it elaborates on the criteria required for uniform-in-time stability of wide sense regenerative processes. New accurate bounds of distribution functions of first occurrence times for regenerative models are also presented.

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Page Count

230

Publisher

CRC Press

Published Date

ISBN 10

0849386411

ISBN 13

9780849386411

Weak Convergence of Measures

By: Vladimir I. Bogachev

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Weak Convergence of Measures

By: Vladimir I. Bogachev

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

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Page Count

301

Publisher

American Mathematical Society

Published Date

ISBN 10

147047798X

ISBN 13

9781470477981

Random Permanents

By: IU. IUrii Vasilevich Borovskikh,Yuri V. Borovskikh,V. Vladimir Semenovich Koroliuk

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Random Permanents

By: IU. IUrii Vasilevich Borovskikh,Yuri V. Borovskikh,V. Vladimir Semenovich Koroliuk

The determination of permanent random measures and the representation of symmetric statistics as functionals of symmetrization random measures with some deterministic kernels, make it possible to clarify the influence of properties of a random measure on the limiting results for symmetric statistics and also to study the influence of the characteristic structure of these kernels. This approach in the theory of symmetric statistics has inspired the authors to investigate random permanents and their generating functions in detail. New limiting results for random permanents are basically obtained by employing the algebraic and analytical properties of the permanents of sampling matrices and their generating functions. This notion allows clarification of different schemes in the asymptotic analysis of symmetric statistics as the size of a sample n tends to infinity.

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Page Count

202

Publisher

VSP

Published Date

ISBN 10

9067641847

ISBN 13

9789067641845

Book's by Vladimir V. Korolyuk

Stochastic Models of Systems

Stochastic Models of Systems

Semi-Markov Random Evolutions

Semi-Markov Random Evolutions

Topics on Regenerative Processes

Topics on Regenerative Processes

Weak Convergence of Measures

Weak Convergence of Measures

Random Permanents

Random Permanents

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