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 Rd. These measures are associated with the family of generalized grey Brownian motions Bβ,α, 0β≤1, 0α≤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 dα>2 and 1α≤2. The Green measure then generalizes those measures of all these classes.

Keywords

• fractional Brownian motion
• generalized grey Brownian motion
• green measure
• subordination