Abstract:

Suppose X is a super-α-stable process in R^d, (0<α<2), whose branching rate function is dt, and branching mechanism is of the form ψ(z)=z^1+β
(0<β≤1). Let X_τ and Y_τ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of X_τ and Y_τ are discussed.

Key words: Super-α-stable process, absolute continuity, exit measure, total weighted occupation time measure