A Transformation for Spectrally Negative Lévy Processes and Applications

Marie Chazal, Andreas E. Kyprianou, Pierre Patie

Research output: Chapter or section in a book/report/conference proceedingChapter or section


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 Poincar’ Probab Statist 47(3):917–928, 2011), Gnedin (Regeneration in Random Combinatorial Structures. arXiv:0901.4444v1 [math.PR]), Patie and Savov (Electron J Probab 17(38):1–22, 2012), as well as in older work of Urbanik (Probab Math Statist 15:493–513, 1995). We show how some specific instances of this mapping prove to be useful for a variety of applications.

Original languageEnglish
Title of host publicationA Lifetime of Excursions Through Random Walks and Lévy Processes
EditorsM. Chazal, A. E. Kyprianou, P. Patie
Place of PublicationCham, Switzerland
Number of pages24
ISBN (Electronic)9783030833091
ISBN (Print)9783030833084
Publication statusE-pub ahead of print - 30 Jul 2021

Publication series

NameProgress in Probability
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428


  • Exponential functional
  • Fluctuation theory
  • Hypergeometric function
  • Intertwining
  • Positive self-similar Markov process
  • Spectrally negative Lévy process

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Mathematical Physics
  • Mathematics (miscellaneous)


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