## Electronic Communications in Probability

### Infinite Divisibility of Gaussian Squares with Non-zero Means

#### 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

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

Rights

#### 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

#### References

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• Marcus, Michael B.; Rosen, Jay. Markov processes, Gaussian processes, and local times. Cambridge Studies in Advanced Mathematics, 100. Cambridge University Press, Cambridge, 2006. x+620 pp. ISBN: 978-0-521-86300-1; 0-521-86300-7
• Marcus, Michael B.; Rosen, Jay. Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $R^2$ with non–zero mean, preprint, (2008), arXiv:0806.3188.