Electronic Communications in Probability

Infinite Divisibility of Gaussian Squares with Non-zero Means

Michael Marcus and Jay Rosen

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Abstract

We give necessary and sufficient conditions for a Gaussian vector with non-zero mean, to have infinitely divisible squares for all scalar multiples of the mean, and show how the this vector is related to the local times of a Markov chain determined by the covariance matrix of the Gaussian vector. Our results add to results of Griffiths, Bapat, Eisenbaum and Kaspi.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 36, 364-376.

Dates
Accepted: 27 June 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233463

Digital Object Identifier
doi:10.1214/ECP.v13-1389

Mathematical Reviews number (MathSciNet)
MR2415144

Zentralblatt MATH identifier
1189.60080

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Gaussian vectors infinite divisibility Markov chains

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Marcus, Michael; Rosen, Jay. Infinite Divisibility of Gaussian Squares with Non-zero Means. Electron. Commun. Probab. 13 (2008), paper no. 36, 364--376. doi:10.1214/ECP.v13-1389. https://projecteuclid.org/euclid.ecp/1465233463


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References

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