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Renewal theory for perturbed random ...

Iksanov, Alexander.

Renewal theory for perturbed random walks and similar processes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Renewal theory for perturbed random walks and similar processesby Alexander Iksanov.
Author:	Iksanov, Alexander.
Published:	Cham :Springer International Publishing :2016.
Description:	xiv, 250 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Random walks (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-49113-4
ISBN:	9783319491134$q(electronic bk.)

Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander.

Renewal theory for perturbed random walks and similar processes[electronic resource] /by Alexander Iksanov. - Cham :Springer International Publishing :2016. - xiv, 250 p. :ill., digital ;24 cm. - Probability and its applications,2297-0371. - Probability and its applications..

Preface -- Perturbed random walks -- Affine recurrences -- Random processes with immigration -- Application to branching random walk -- Application to the Bernoulli sieve -- Appendix -- Bibliography.

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.

ISBN: 9783319491134$q(electronic bk.)

Standard No.: 10.1007/978-3-319-49113-4doiSubjects--Topical Terms:

183715
Random walks (Mathematics)

LC Class. No.: QA274.73

Dewey Class. No.: 519.282

Renewal theory for perturbed random walks and similar processes
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