The Annals of Probability

A characterization of the infinitely divisible squared Gaussian processes

Nathalie Eisenbaum and Haya Kaspi

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Abstract

We show that, up to multiplication by constants, a Gaussian process has an infinitely divisible square if and only if its covariance is the Green function of a transient Markov process.

Article information

Source
Ann. Probab., Volume 34, Number 2 (2006), 728-742.

Dates
First available in Project Euclid: 9 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1147179987

Digital Object Identifier
doi:10.1214/009117905000000684

Mathematical Reviews number (MathSciNet)
MR2223956

Zentralblatt MATH identifier
1102.60031

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions 60G15: Gaussian processes 60J25: Continuous-time Markov processes on general state spaces 60J55: Local time and additive functionals

Keywords
Gaussian processes infinite divisibility Markov processes local time

Citation

Eisenbaum, Nathalie; Kaspi, Haya. A characterization of the infinitely divisible squared Gaussian processes. Ann. Probab. 34 (2006), no. 2, 728--742. doi:10.1214/009117905000000684. https://projecteuclid.org/euclid.aop/1147179987


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