Electronic Journal of Probability

Inequalities for permanental processes

Nathalie Eisenbaum

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 99, 15 pp.

Accepted: 18 November 2013
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60E15: Inequalities; stochastic orderings

Permanental process Gaussian process infinite divisibility Slepian lemma concentration inequality

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Eisenbaum, Nathalie. Inequalities for permanental processes. Electron. J. Probab. 18 (2013), paper no. 99, 15 pp. doi:10.1214/EJP.v18-2919. https://projecteuclid.org/euclid.ejp/1465064324

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