Renewal Theory for Perturbed Random Walks and Similar Processes

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 insur...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Iksanov, Alexander (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
Edición:1st ed. 2016.
Colección:Probability and Its Applications,
Temas:
Probabilities.
Probability Theory.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Renewal Theory for Perturbed Random Walks and Similar Processes  |h [electronic resource] /  |c by Alexander Iksanov. 
250 |a 1st ed. 2016. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Birkhäuser,  |c 2016. 
300 |a XIV, 250 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Probability and Its Applications,  |x 2297-0398 
505 0 |a Preface -- Perturbed random walks -- Affine recurrences -- Random processes with immigration -- Application to branching random walk -- Application to the Bernoulli sieve -- Appendix -- Bibliography. 
520 |a 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. 
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950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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