Moments of last exit times for Lévy processes
Ken-Iti Sato, Toshiro Watanabe (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Ken-Iti Sato, Toshiro Watanabe (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Emmanuel Jacob (2010)
Annales de l'I.H.P. Probabilités et statistiques
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The integrated brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which...
Zbyněk Pawlas (2003)
Kybernetika
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Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.
Anthony G. Pakes (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)
Annales de l'I.H.P. Probabilités et statistiques
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In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than for 1≥>0.