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A Lifetime of Excursions Through Random Walks and Lévy Processes

A Volume in Honour of Ron Doney’s 80th Birthday

  • Book
  • © 2021

Overview

Editors:
  1. Loïc Chaumont

    1. LAREMA, Université d’Angers, Angers, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Andreas E. Kyprianou

    1. Department of Mathematical Sciences, University of Bath, Bath, UK

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    You can also search for this editor in PubMed   Google Scholar

  • Includes an overview over Ron Doney's scientific achievements
  • Presents research articles from renowned researchers
  • Covers research fields influenced by Ron Doney

Part of the book series: Progress in Probability (PRPR, volume 78)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-vi
    Download chapter PDF

  2. A Lifetime of Excursions Through Random Walks and Lévy Processes

    • Loïc Chaumont, Andreas E. Kyprianou
    Pages 1-11

  3. Path Decompositions of Perturbed Reflecting Brownian Motions

    • Elie Aïdékon, Yueyun Hu, Zhan Shi
    Pages 13-42

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

    • Larbi Alili, Carine Bartholmé, Loïc Chaumont, Pierre Patie, Mladen Savov, Stavros Vakeroudis
    Pages 43-58

  5. On a Two-Parameter Yule-Simon Distribution

    • Erich Baur, Jean Bertoin
    Pages 59-82

  6. The Limit Distribution of a Singular Sequence of Itô Integrals

    • Denis Bell
    Pages 83-86

  7. On Multivariate Quasi-infinitely Divisible Distributions

    • David Berger, Merve Kutlu, Alexander Lindner
    Pages 87-120

  8. Extremes and Regular Variation

    • Nick H. Bingham, Adam J. Ostaszewski
    Pages 121-137

  9. Some New Classes and Techniques in the Theory of Bernstein Functions

    • Safa Bridaa, Sonia Fourati, Wissem Jedidi
    Pages 139-155

  10. A Transformation for Spectrally Negative Lévy Processes and Applications

    • Marie Chazal, Andreas E. Kyprianou, Pierre Patie
    Pages 157-180

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

    • Denis Denisov, Alexander Sakhanenko, Vitali Wachtel
    Pages 181-203

  12. On Local Times of Ornstein-Uhlenbeck Processes

    • Nathalie Eisenbaum
    Pages 205-213

  13. Two Continua of Embedded Regenerative Sets

    • Steven N. Evans, Mehdi Ouaki
    Pages 215-230

  14. No-Tie Conditions for Large Values of Extremal Processes

    • Yuguang Ipsen, Ross Maller
    Pages 231-243

  15. Slowly Varying Asymptotics for Signed Stochastic Difference Equations

    • Dmitry Korshunov
    Pages 245-267

  16. The Doob–McKean Identity for Stable Lévy Processes

    • Andreas E. Kyprianou, Neil O’Connell
    Pages 269-282

  17. Oscillatory Attraction and Repulsion from a Subset of the Unit Sphere or Hyperplane for Isotropic Stable Lévy Processes

    • Mateusz Kwaśnicki, Andreas E. Kyprianou, Sandra Palau, Tsogzolmaa Saizmaa
    Pages 283-313

  18. Angular Asymptotics for Random Walks

    • Alejandro López Hernández, Andrew R. Wade
    Pages 315-342

  19. First Passage Times of Subordinators and Urns

    • Philippe Marchal
    Pages 343-355
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Keywords

About this book

This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.

Editors and Affiliations

  • LAREMA, Université d’Angers, Angers, France

    Loïc Chaumont

  • Department of Mathematical Sciences, University of Bath, Bath, UK

    Andreas E. Kyprianou

About the editors

Loïc Chaumont was educated at Université du Maine (Le Mans) and Université Paris 6 and is currently a professor of mathematics at Université d'Angers. He published over 50 research papers on theory of stochastic processes, both in discrete and continuous times. His main domain of research concerns Lévy processes. He was the director of LAREMA, the CNRS mathematics research unit in Angers, from 2012 to 2016.

Andreas E. Kyprianou was educated at the University of Oxford and University of Sheffield and is currently a professor of mathematics at the University of Bath. He has spent over 25 years working on the theory and application of path-discontinuous stochastic processes and has over 130 publications, including two graduate textbooks on Lévy processes. During his time in Bath he co-founded and directed the Prob-L@B (Probability Laboratory at Bath), was PI for a multi-million pound EPSRC Centre for Doctoral Training and is currently the Director of the Bath Institute for Mathematical Innovation.

Bibliographic Information

  • Book Title: A Lifetime of Excursions Through Random Walks and Lévy Processes

  • Book Subtitle: A Volume in Honour of Ron Doney’s 80th Birthday

  • Editors: Loïc Chaumont, Andreas E. Kyprianou

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-3-030-83309-1

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-83308-4Published: 01 December 2021

  • Softcover ISBN: 978-3-030-83311-4Published: 02 December 2022

  • eBook ISBN: 978-3-030-83309-1Published: 01 January 2022

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: VI, 355

  • Number of Illustrations: 7 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes, Combinatorics

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