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Discrete-Time Semi-Markov Random Evolutions and Their Applications

  • Book
  • © 2023

Overview

Authors:
  1. Nikolaos Limnios

    1. Laboratoire de Mathématiques Appliquées, Sorbonne University Alliance, Université de Technologie de Compiègne, Compiègne, France

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    You can also search for this author in PubMed   Google Scholar

  2. Anatoliy Swishchuk

    1. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Extends the theory of semi-Markov chains to random evolutions in discrete time
  • Presents limit theorems for random evolutions in different schemes
  • Shows applications in epidemiology and finance

Part of the book series: Probability and Its Applications (PA)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Discrete-Time Stochastic Calculus in Banach Space

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 1-17

  3. Discrete-Time Semi-Markov Chains

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 19-41

  4. Discrete-Time Semi-Markov Random Evolutions

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 43-54

  5. Weak Convergence of DTSMRE in Series Scheme

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 55-81

  6. DTSMRE in Reduced Random Media

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 83-99

  7. Controlled Discrete-Time Semi-Markov Random Evolutions

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 101-137

  8. Epidemic Models in Random Media

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 139-156

  9. Optimal Stopping of Geometric Markov Renewal Chains and Pricing

    • Nikolaos Limnios, Anatoliy Swishchuk
    Pages 157-175

  10. Back Matter

    Pages 177-198
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Keywords

About this book

This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

Authors and Affiliations

  • Laboratoire de Mathématiques Appliquées, Sorbonne University Alliance, Université de Technologie de Compiègne, Compiègne, France

    Nikolaos Limnios

  • Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Anatoliy Swishchuk

About the authors

Nikolaos Limnios is a Professor at the Applied Mathematics Laboratory at the Université de Technologie de Compiègne, France. His research interests include stochastic processes, random evolutions, with a focus on semi-Markov processes, and statistics, and applications in reliability, biology, seismology, insurance, and finance. He has published more than 150 journal articles and 10 books on the theory and applications of stochastic processes and statistics. He serves on editorial boards for several research journals.

Anatoliy Swishchuk is a Professor in Mathematical Finance at the Department of Mathematics and Statistics, University of Calgary, Canada. His research areas include financial mathematics, random evolutions and their applications, biomathematics, and stochastic calculus. He serves on editorial boards for several research journals and is the author of more than 180 publications, including 15 books and more than 120 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award.

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