Superprocesses (under the name continuous state branchingprocesses) appeared, first, in a pioneering work of S.Watanabe [J. Math. Kyoto Univ. 8 (1968)141 –167 ]. Deep results on paths of the super-Brownian motion were obtained by Dawson, Perkins, Le Gall and others.
In earlier papers, a superprocess was interpreted as a Markov process $X_t$ in the space of measures. This is not sufficient for a probabilistic approach to boundary value problems. A reacher model based on the concept of exit measures was introduced by E.B.Dynkin [Probab. Theory Related Fields 89 (1991) 89 –115 ]. A model of a superprocess as a system of exit measures from time-space open sets was systematically developed in 1993 [E.B. Dynkin, Ann.Probab. 21 (1993)1185 –1262 ]. In particular, branchingand Markov properties of such a system were established and used to investigate partial differential equations. In the present paper, we show that the entire theory of superprocesses can be deduced from these properties.
"Branching Exit Markov Systems and Superprocesses." Ann. Probab. 29 (4) 1833 - 1858, October 2001. https://doi.org/10.1214/aop/1015345774