On the Lamperti stable processes

2008/02/06 by M. E. Caballero, J. C. Pardo, Caballero, M. E. +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60E07 #60G51 #60G52 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60E07 #msc:60G51 #msc:60G52

paper · pdf · doi:10.48550/arxiv.0802.0851

6 figures

openalex publication_date 2008/02/06 · arxiv created 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a new family of \R^d-valued Lévy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitely (see for instance \citecc, \citeckp, \citekp and \citepp). This family of processes shares many properties with the tempered stable and the layered stable processes, defined in Rosiński \citero and Houdré and Kawai \citehok respectively, for instance their short and long time behaviour. Additionally, in the real valued case we find a series representation which is used for sample paths simulation. In this work we find general properties of this class and we also provide many examples, some of which appear in recent literature.

Citations

• Law of the exponential functional of a new family of one-sided Levy processes via self-similar continuous state branching processes with immigration and the Wright hypergeometric functions
• Foundations of Modern Probability
• Special, conjugate and complete scale functions for spectrally negative Lévy processes

Cited by

• Schauder estimates for degenerate Lévy Ornstein-Ulhenbeck operators

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