On the Lamperti stable processes

By María Emilia Caballero, Juan Carlos Pardo, José-Luis Pérez. 2008

52 citations recorded by the source corpus.

We consider a new family of IR d -valued L evy 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. Here, in the one dimensional case we provide an explicit form for the characteristic exponent and other several useful properties of the class (for some particular cases see [6], [10], [24] and [28]). This family of processes shares many properties with the tempered stable and the layered stable processes, dened in Rosi nski [31] and Houdr e and Kawai [16] respectively, for instance their short and long time behavior. We also nd a series representation which is used for sample path simulation, illustrated in the case d = 1. Finally we provide many examples, some of which appear in recent literature.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6ac0818941e92953d9738bb95fe509800d4413d8

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Citations in the corpus

Coupling property and gradient estimates of L\'{e}vy processes via the symbol (2010, unknown): “(5) Lamperti stable processes ([4]): Q(θ, s) = s exp(sf(θ)) s (es − 1)1+α ,”
Law of the absorption time of some positive self-similar Markov processes (2009, methodology): “X is then a positive self-similar Feller process and the characteristic triplet of the underlying Lévy process has been computed by Caballero and Chaumont [12], see also [13] and [23], for an expression of its characteristic exponent in terms of the Pochhammer symbol.”
The Lamperti representation of real-valued self-similar Markov processes (2011, background): “For the definition and properties of Lamperti-stable processes, see [5].”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “[8] and [27] and two-sided processes were studied in [11], [ 12 ], [14] and [22].”
Meromorphic Lévy processes and their fluctuation identities. (2010, background): “We mention in particular the many cases of spectrally negative Lévy processes in [21, 32], hyper-exponential and generalized hyper-exponential Lévy processes [24], Lamperti-stable processes in [9, 10, 13, 39], Hypergeometric processes in [35, 31, 11], β-processes in [29] and θ-processes in [30].”