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Inequalities for permanental processes. (English) Zbl 1290.60044
Summary: Permanental processes are a natural extension of the definition of squared Gaussian processes. Each one-dimensional marginal of a permanental process is a squared Gaussian variable, but there is not always a Gaussian structure for the entire process. The interest to better know them is highly motivated by the connection established by Eisenbaum and Kaspi, between the infinitely divisible permanental processes and the local times of Markov processes. Unfortunately the lack of Gaussian structure for general permanental processes makes their behavior hard to handle. We present here an analogue for infinitely divisible permanental vectors, of some well-known inequalities for Gaussian vectors.
MSC:
60G15 Gaussian processes
60E07 Infinitely divisible distributions; stable distributions
60E15 Inequalities; stochastic orderings
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