Electronic Journal of Probability

Decompositions of infinitely divisible nonnegative processes

Nathalie Eisenbaum

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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