Branching exit Markov systems and superprocesses (Q1872249)

Deep results on constructions and properties of superprocesses were obtained by D. A. Dawson, E. A. Perkins, J.-F. Le Gall, S. Watanabe and many others including the author. In earlier papers, a superprocess was interpreted as a Markov process in the space of measures. This is not sufficient a probabilistic approach to boundary value problems. A reacher model based on the concept of exit measures is introduced by the author [Probab. Theory Relat. Fields 89, No. 1, 89-115 (1991; Zbl 0722.60062)]. A model of a superprocess as a system of exit measures from time-space open sets were systematically developed by the author [Ann. Probab. 21, No. 3, 1185-1262 (1993; Zbl 0806.60066)]. In particular, branching and Markov properties of such a system were established and used to investigate partial differential equations. In the present paper, it is shown that the entire theory of superprocesses can be deduced from these properties.