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A Lifetime of Excursions Through Random Walks and Lévy Processes

Part of the Progress in Probability Book Series (volume 78)

Editors: Chaumont, Loïc; Kyprianou, Andreas E.

DOI: 10.1007/978-3-030-83309-1

ISBN: 978-3-030-83308-4

Publisher: Springer International Publishing - Springer Journals

Jul 30, 2021

1 - 10 of 18 Chapters

Available

A Lifetime of Excursions Through Random Walks and Lévy Processes

Chaumont, Loïc; Kyprianou, Andreas E.

Pages: 1 –11

[We recall the many highlights of Professor Ron Doney’s career summarising his main contributions to the theory of random walks and Lévy processes.]
Available

Path Decompositions of Perturbed Reflecting Brownian Motions

Aïdékon, Elie; Hu, Yueyun; Shi, Zhan

Pages: 13 –42

[We are interested in path decompositions of a perturbed reflecting Brownian motion (PRBM) at the hitting times and at the minimum. Our study relies on the loop soups developed by Lawler and Werner (Probab Theory Relat Fields 4:197–217, 2004) and Le Jan (Ann Probab 38:1280–1319, 2010; Markov...
Available

On Doney’s Striking Factorization of the Arc-Sine Law

Alili, Larbi; Bartholmé, Carine; Chaumont, Loïc; Patie, Pierre; Savov, Mladen; Vakeroudis, Stavros

Pages: 43 –58

[In Doney (Bull Lond Math Soc 19(2):177–182, 1987), R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a...
Available

On a Two-Parameter Yule-Simon Distribution

Baur, Erich; Bertoin, Jean

Pages: 59 –82

[We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin (J Stat Phys 176(3):679–691, 2019) in the context of a preferential attachment algorithm with fading memory. By making the link to a general branching process with...
Available

The Limit Distribution of a Singular Sequence of Itô Integrals

Bell, Denis

Pages: 83 –86

[We give an alternative, elementary proof of a result of Peccati and Yor concerning the limit law of a sequence of Itô integrals with integrands having singular asymptotic behavior.]
Available

On Multivariate Quasi-infinitely Divisible Distributions

Berger, David; Kutlu, Merve; Lindner, Alexander

Pages: 87 –120

[A quasi-infinitely divisible distribution on ℝd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
Available

Extremes and Regular Variation

Bingham, Nick H.; Ostaszewski, Adam J.

Pages: 121 –137

[We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the point of view of our recent work on general regular variation.]
Available

Some New Classes and Techniques in the Theory of Bernstein Functions

Bridaa, Safa; Fourati, Sonia; Jedidi, Wissem

Pages: 139 –155

[In this paper we provide some new properties that are complementary to the book of Schilling-Song-Vondraček (Bernstein functions, 2nd edn. De Gruyter, Berlin, 2012).]
Available

A Transformation for Spectrally Negative Lévy Processes and Applications

Chazal, Marie; Kyprianou, Andreas E.; Patie, Pierre

Pages: 157 –180

[The aim of this work is to extend and study a family of transformations between Laplace exponents of Lévy processes which have been introduced recently in a variety of different contexts, Patie (Bull Sci Math 133(4):355–382, 2009; Bernoulli 17(2):814–826, 2011), Kyprianou and Patie (Ann Inst H...
Available

First-Passage Times for Random Walks in the Triangular Array Setting

Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali

Pages: 181 –203

[In this paper we continue our study of exit times for random walks with independent but not necessarily identically distributed increments. Our paper “First-passage times for random walks with non-identically distributed increments” (2018) was devoted to the case when the random walk is...

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