Electronic Communications in Probability

Infinite Divisibility of Gaussian Squares with Non-zero Means

Michael Marcus and Jay Rosen

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Gaussian vectors infinite divisibility Markov chains

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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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