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2019 Decompositions of infinitely divisible nonnegative processes
Nathalie Eisenbaum
Electron. J. Probab. 24(none): 1-25 (2019). DOI: 10.1214/19-EJP367

Abstract

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.

Citation

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Nathalie Eisenbaum. "Decompositions of infinitely divisible nonnegative processes." Electron. J. Probab. 24 1 - 25, 2019. https://doi.org/10.1214/19-EJP367

Information

Received: 25 October 2018; Accepted: 18 September 2019; Published: 2019
First available in Project Euclid: 2 October 2019

zbMATH: 07142903
MathSciNet: MR4017127
Digital Object Identifier: 10.1214/19-EJP367

Subjects:
Primary: 60E07, 60G15, 60G51, 60J25, 60J55, 69G17

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