Infinite Divisibility of Gaussian Squares with Non-zero Means
Michael B. Marcus, The City College of CUNY
Jay Rosen, The College of Staten Island of CUNY
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.
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