ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES*

Suppose X is a super-α-stable process in Rd, (0 < α < 2), whose branching rate function is dt, and branching mechanism is of the form Ψ(z) = z1+β. Let Xτ and Yτ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xτ and Yτ are discussed.