© 2017

Nonlinearly Perturbed Semi-Markov Processes


  • Contains an extended bibliography of works in the areas

  • Essential reference for theoretical and applied researchers

  • Allows use with mixed-level classes for doctoral and advanced undergraduate students


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


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. 


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

Authors and affiliations

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

About the authors

Dmitrii Silvestrov: Candidate of Science [eq. PhD], (1969, Kiev University), Doctor of Science (1972, Kiev University), Professor at Kiev University (1974-1992), Mälardalen University (1999-2009) and Stockholm University from 2009. The main areas of research are stochastic processes and actuarial and financial mathematics. Author of 10 books and more than 140 research papers, co-editor of 15 collective books and proceedings. Supervised 22 doctoral students who subsequently obtained eq. PhD and PhD degrees.

Sergei Silvestrov: PhD (1996, Umeå University), Docent at Lund University (2002-2011), Professor at Mälardalen University from 2011. The main areas of research are non-commutative analysis and geometry and applied matrix analysis. Author of 1 book and more than 120 research papers, co-editor of 15 collective books and proceedings. Supervised 6 doctoral students who subsequently obtained PhD degrees.

Bibliographic information

  • Book Title Nonlinearly Perturbed Semi-Markov Processes
  • Authors Dmitrii Silvestrov
    Sergei Silvestrov
  • Series Title SpringerBriefs in Probability and Mathematical Statistics
  • Series Abbreviated Title SpringerBriefs in Probabil., Math.Statist.
  • DOI
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-60987-4
  • eBook ISBN 978-3-319-60988-1
  • Series ISSN 2365-4333
  • Series E-ISSN 2365-4341
  • Edition Number 1
  • Number of Pages XIV, 143
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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“This book is aimed at studying asymptotic expansions for moment hitting times, stationary and conditional quasi-stationary distributions, and various further functionals, for nonlinearly perturbed semi-Markov processes having finite phase space. … The bibliography is broad and relevant, and includes various publications of the authors thanks to their wide expertise on the topics under investigation. … book is of interest to researchers working on semi-Markov processes, and provides a useful reference for investigations dealing with asymptotic problems for perturbed stochastic processes.” (Antonio Di Crescenzo, Mathematical Reviews, July, 2018)