Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 109, 25 pp.
Decompositions of infinitely divisible nonnegative processes
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.
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
Permanent link to this document
Digital Object 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
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