Electronic Journal of Probability

Decompositions of infinitely divisible nonnegative processes

Nathalie Eisenbaum

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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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 109, 25 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1569981824

Digital Object Identifier
doi:10.1214/19-EJP367

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions 60G15: Gaussian processes 69G17 60G51: Processes with independent increments; Lévy processes 60J25: Continuous-time Markov processes on general state spaces 60J55: Local time and additive functionals

Keywords
infinitely divisible process Lévy measure permanental process local time Markov process Gaussian process

Rights
Creative Commons Attribution 4.0 International License.

Citation

Eisenbaum, Nathalie. Decompositions of infinitely divisible nonnegative processes. Electron. J. Probab. 24 (2019), paper no. 109, 25 pp. doi:10.1214/19-EJP367. https://projecteuclid.org/euclid.ejp/1569981824


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