Probability and Its Applications

Renewal Theory for Perturbed Random Walks and Similar Processes

Authors: Iksanov, Alexander

  • 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
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  • ISBN 978-3-319-49113-4
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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.

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-319-49113-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-49111-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Renewal Theory for Perturbed Random Walks and Similar Processes
Authors
Series Title
Probability and Its Applications
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-49113-4
DOI
10.1007/978-3-319-49113-4
Hardcover ISBN
978-3-319-49111-0
Series ISSN
2297-0371
Edition Number
1
Number of Pages
XIV, 250
Topics