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Article Dans Une Revue Electronic Journal of Probability Année : 2019

Decompositions of infinitely divisible nonnegative processes

Résumé

We establish decomposition formulas for nonnegative infinitely divisible processes. They allow to give an explicit expression of their Lévy measure. In the special case of infinitely divisible permanental processes, one of these decompositions represents a new isomorphism theorem involving the local time process of a transient Markov process. We obtain in this case the expression of the Lévy measure of the total local time process which is in itself a new result on the local time process. Finally, we identify a determining property of the local times for their connection with permanental processes.
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Dates et versions

hal-02322980 , version 1 (21-10-2019)

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Nathalie Eisenbaum. Decompositions of infinitely divisible nonnegative processes. Electronic Journal of Probability, 2019, 24, ⟨10.1214/19-EJP367⟩. ⟨hal-02322980⟩
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