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.