Renewal Theory for Perturbed Random Walks and Similar Processes

  • Alexander Iksanov

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

Introduction

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

Authors and affiliations

  • Alexander Iksanov
    • 1
  1. 1.Faculty of CyberneticsT. Shevchenko National University KyivKievUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-49113-4
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-49111-0
  • Online ISBN 978-3-319-49113-4
  • Series Print ISSN 2297-0371
  • Series Online ISSN 2297-0398
  • About this book