Branching exit Markov systems and superprocesses
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.
scientific article; zbMATH DE number 1906042