  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 $B_{\beta,\alpha}$, $0<\beta\le1$,
$0<\alpha\le2$. 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 $1<\alpha\le2$. The Green
measure then generalizes those measures of all these classes.
