Some explicit identities associated with positive self-similar Markov processes.

By L. Chaumont, Andreas E. Kyprianou, Juan Carlos Pardo Millan. 2007

61 citations recorded by the source corpus.

We consider some special classes of Levy processes with no gaussian component whose Levy measure is of the type , where [nu] is the density of the stable Levy measure and [gamma] is a positive parameter which depends on its characteristics. These processes were introduced in [M. E. Caballero, L. Chaumont, Conditioned stable Levy processes and the Lamperti representation, J. Appl. Probab. 43 (2006) 967-983] as the underlying Levy processes in the Lamperti representation of conditioned stable Levy processes. In this paper, we compute explicitly the law of these Levy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/791ea8f81cdae3a7f4f04d79d319bb2119a0a452

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Citations in the corpus

The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “See Caballero et al. [26] and Kyprianou and Pardo [67] for further computations in this spirit and Lambert [73] for further applications in population biology.”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “Lamperti-stable processes is a particularly interesting subclass of the -family since it oers many examples of uctuation identities related to Wiener-Hopf factorization which can be computed in closed form, see [11], [ 14 ] and [22].”
On the Lamperti stable processes (2008, background): “- In the papers [9] , [23], [31] the main processes in study are Lamperti stable processes.”
Special, conjugate and complete scale functions for spectrally negative Lévy processes (2007, background): “[14] and Section 3 of Patie [45] that this is the Laplace exponent of a spectrally negative Lévy process.”
General tax Structures and the Lévy Insurance Risk Model (2009, unknown): “See, for example, [8], [9], [15], and [17].”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “Recent work however has produced many completely explicit examples of scale functions (e.g.: Hubalek and Kyprianou, 2008; Patie, 2008; Chaumont, Kyprianou and Pardo, 2009 ) and in particular Hubalek and Kyprianou (2008); Kyprianou and Rivero (2008); Kyprianou and Patie (2008) outline a method from ”