We study a specific particle system in which particles undergo
random branchingand spatial motion. Such systems are best described,
mathematically, via measure valued stochastic processes. As is now quite
standard, we study the so-called superprocess limit of such a system as both
the number of particles in the system and the branchingrate tend to infinity.
What differentiates our system from the classical superprocess case, in which
the particles move independently of each other, is that the motions of our
particles are affected by the presence of a global stochastic flow. We
establish weak convergence to the solution of a well-posed martingale problem.
Usingthe particle picture formulation of the flow superprocess, we study some
of its properties. We give formulas for its first two moments and consider two
macroscopic quantities describing its average behavior, properties that have
been studied in some detail previously in the pure flow situation, where
branching was absent. Explicit formulas for these quantities are given and
graphs are presented for a specific example of a linear flow of
Ornstein–Uhlenbeck type.