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.
- Book Title Renewal Theory for Perturbed Random Walks and Similar Processes
- Series Title Probability and Its Applications
- Series Abbreviated Title Probability,its Applications
- 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 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
Probability Theory and Stochastic Processes
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