SpringerBriefs in Probability and Mathematical Statistics

Nonlinearly Perturbed Semi-Markov Processes

Authors: Silvestrov, Dmitrii, Silvestrov, Sergei

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  • ISBN 978-3-319-60988-1
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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. 


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.

Table of contents (6 chapters)

  • Introduction

    Silvestrov, Dmitrii (et al.)

    Pages 1-15

  • Laurent Asymptotic Expansions

    Silvestrov, Dmitrii (et al.)

    Pages 17-35

  • Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes

    Silvestrov, Dmitrii (et al.)

    Pages 37-66

  • Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes

    Silvestrov, Dmitrii (et al.)

    Pages 67-79

  • Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes

    Silvestrov, Dmitrii (et al.)

    Pages 81-106

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-60988-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-60987-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinearly Perturbed Semi-Markov Processes
Authors
Series Title
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-60988-1
DOI
10.1007/978-3-319-60988-1
Softcover ISBN
978-3-319-60987-4
Series ISSN
2365-4333
Edition Number
1
Number of Pages
XIV, 143
Number of Illustrations and Tables
3 b/w illustrations
Topics