``On the infinite divisibility of squared Gaussian processes''

Nathalie Eisenbaum, Université Paris, VI

There exist several characterizations of the Gaussian processes with infinitely divisible squares. Nevertheless, except for the Brownian motion, there were no examples, in the literature, of processes satisfying this remarkable property nor examples of processes lacking this property. We will show that the family of fractional Brownian motions provides examples of the two kinds. In view of these examples, we will see that this property actually characterizes a class of Gaussian processes connected via their covariance to Markov processes.

This talk is based on a joint work with H. Kaspi.