Some absolute continuities of superdiffusions and super-stable processes

Zhao Xue-Lei

Stochastic Processes and their Applications, 1994, vol. 50, issue 1, 21-35

Abstract: A superprocess is uniquely determined by a right Markov process and a branching characteristic. As a random measure, a typical question for a superprocess is about its absolute continuity and this kind of questions has been studied by many authors. In this paper, we investigate the absolute continuity on the surface of a smooth domain of d for a class of super-diffusions. We prove that when d = 2 the absolute continuity always holds, and when d [greater-or-equal, slanted] 3 the continuity depends on the branching characteristics and we present a sufficient condition. Moreover, we also consider the absolute continuity of super-diffusions and super-stable processes restricted on non-branching sets. On comparison with previous authors, we further demonstrate the influence of branching characteristics on the local structure of superprocesses from a different angle.

Date: 1994
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