© 2016

Renewal Theory for Perturbed Random Walks and Similar Processes


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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Alexander Iksanov
    Pages 1-41
  3. Alexander Iksanov
    Pages 43-86
  4. Alexander Iksanov
    Pages 87-178
  5. Alexander Iksanov
    Pages 179-189
  6. Alexander Iksanov
    Pages 191-208
  7. Alexander Iksanov
    Pages 209-236
  8. Back Matter
    Pages 237-250

About this book


This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade.

The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters four and five address branching random walks and the Bernoulli sieve, respectively, and their connection to the results of the previous chapters.

With many motivating examples, this book appeals to both theoretical and applied probabilists.


Bernoulli sieve branching random walk limit theorems perpetuities random processes random walks Bernoulli sieve renewal theory

Authors and affiliations

  1. 1.Faculty of CyberneticsT. Shevchenko National University KyivKievUkraine

Bibliographic information

  • Book Title Renewal Theory for Perturbed Random Walks and Similar Processes
  • Authors Alexander Iksanov
  • Series Title Probability and Its Applications
  • Series Abbreviated Title Probability,its Applications
  • DOI
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-49111-0
  • Softcover ISBN 978-3-319-84085-7
  • eBook ISBN 978-3-319-49113-4
  • Series ISSN 2297-0371
  • Series E-ISSN 2297-0398
  • Edition Number 1
  • Number of Pages XIV, 250
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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“The book also has an extensive bibliography with useful references to the relevant chapters. The book is well documented as one can see also looking at the bibliographic comments and the bibliography. The material covered in the book is broad in its scope, the exposition is lucid and friendly. Thus, the text will be of considerable interest for university professors and students.” (Zdzisław Rychlik, zbMATH 1382.60004, 2018)