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Abstract: We consider a new family of $\R^d$-valued L\-{e}vy processes that we callLamperti stable. One of the advantages of this class is that the law of manyrelated functionals can be computed explicitely see for instance \cite{cc},\cite{ckp}, \cite{kp} and \cite{pp}. This family of processes shares manyproperties with the tempered stable and the layered stable processes, definedin Rosi\-nski \cite{ro} and Houdr\-e and Kawai \cite{hok} respectively, forinstance their short and long time behaviour. Additionally, in the real valuedcase 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 manyexamples, some of which appear in recent literature.

Author: M.E. Caballero, J.C. Pardo, J.L. Pérez

Source: https://arxiv.org/

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