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Nonlinearly Perturbed Semi-Markov Processes

  • Dmitrii Silvestrov
  • Sergei Silvestrov

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Dmitrii Silvestrov, Sergei Silvestrov
    Pages 1-15
  3. Dmitrii Silvestrov, Sergei Silvestrov
    Pages 17-35
  4. Dmitrii Silvestrov, Sergei Silvestrov
    Pages 81-106
  5. Dmitrii Silvestrov, Sergei Silvestrov
    Pages 107-121
  6. Back Matter
    Pages 123-143

About this book

Introduction

The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come. 


Keywords

Semi-Markov Process Markov Chain Birth-death Process Nonlinear Perturbation Asymptotic Expansion

Authors and affiliations

  • Dmitrii Silvestrov
    • 1
  • Sergei Silvestrov
    • 2
  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.Division of Applied Mathematics, School of Education, Culture and Communication (UKK)Mälardalen UniversityVästeråsSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-60988-1
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-60987-4
  • Online ISBN 978-3-319-60988-1
  • Series Print ISSN 2365-4333
  • Series Online ISSN 2365-4341
  • Buy this book on publisher's site