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  • © 2016

Renewal Theory for Perturbed Random Walks and Similar Processes

Birkhäuser

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  • Provides a thorough discussion of the state-of-the art in the area with a special emphasis on the methods employed

  • Gives results in a final form and poses a number of open questions at the same time

  • Discusses numerous examples and applications

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

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  • ISBN: 978-3-319-49113-4
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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
  2. Perturbed Random Walks

    • Alexander Iksanov
    Pages 1-41
  3. Perpetuities

    • Alexander Iksanov
    Pages 43-86
  4. Random Processes with Immigration

    • Alexander Iksanov
    Pages 87-178
  5. Application to Branching Random Walk

    • Alexander Iksanov
    Pages 179-189
  6. Application to the Bernoulli Sieve

    • Alexander Iksanov
    Pages 191-208
  7. Appendix

    • 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.

Keywords

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

Reviews

“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)

Authors and Affiliations

  • Faculty of Cybernetics, T. Shevchenko National University Kyiv, Kiev, Ukraine

    Alexander Iksanov

Bibliographic Information

  • Book Title: Renewal Theory for Perturbed Random Walks and Similar Processes

  • Authors: Alexander Iksanov

  • Series Title: Probability and Its Applications

  • DOI: https://doi.org/10.1007/978-3-319-49113-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2016

  • 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

  • Topics: Probability Theory

Buying options

eBook
USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-49113-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 119.99
Price excludes VAT (USA)
Hardcover Book
USD 119.99
Price excludes VAT (USA)