Green Measures for a Class of non-Markov Processes

Abstract

In this paper, we investigate the Green measure for a class of non-Gaussian processes in ${\mathbb{R}}^d$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta ,\alpha }$, $0<\beta \le 1$, $0<\alpha \le 2$. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability $1$ for $d\alpha >2$ and $1<\alpha \le 2$. The Green measure then generalizes those measures of all these classes.

arXiv comment13 pages