Characterization of positively correlated squared Gaussian processes

N. Eisenbaum (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We solve a conjecture raised by Evans in 1991 on the characterization of the positively correlated squared Gaussian vectors. We extend this characterization from squared Gaussian vectors to permanental vectors. As side results, we obtain several equivalent formulations of the property of infinite divisibility for squared Gaussian processes.

Domaines: Probabilités [math.PR]

N. Eisenbaum. Characterization of positively correlated squared Gaussian processes. Annals of Probability, 2014, 42 (2), pp.559-575. ⟨10.1214/12-AOP807⟩. ⟨hal-00988168⟩