ON LAMPERTI STABLE PROCESSES
M. E. Caballero
J. C. Pardo
J. L. Pérez
Abstract: In this paper, we consider a new family of -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 explicitly. In the one-dimensional case we provide an explicit
form for the characteristic exponent and other several useful properties of the class. This
family of processes shares many tractable properties with the tempered stable and the layered
stable processes, defined by Rosiński [33] and Houdré and Kawai [16], respectively. We also
find a series representation which is used for sample path simulation, illustrated in the case
. Finally, we provide many examples, some of which appear in recent literature.
2000 AMS Mathematics Subject Classification: Primary: 60E07; Secondary: 60G51,
60G52.
Keywords and phrases: Lamperti stable distributions and processes, stable processes,
Lévy processes.