Overview
- 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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Table of contents (6 chapters)
Keywords
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 withand 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.
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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: 978-3-319-49111-0Published: 18 January 2017
Softcover ISBN: 978-3-319-84085-7Published: 30 April 2018
eBook ISBN: 978-3-319-49113-4Published: 09 December 2016
Series ISSN: 2297-0371
Series E-ISSN: 2297-0398
Edition Number: 1
Number of Pages: XIV, 250