The main objective of this work is to study a natural class of catalytic
Ornstein-Uhlenbeck (O-U) processes with a measure-valued random catalyst, for
example, super-Brownian motion. We relate this to the class of affine processes
that provides a unified setting in which to view Ornstein-Uhlenbeck processes,
superprocesses, and Ornstein-Uhlenbeck processes with superprocess catalyst. We
then review some basic properties of super-Brownian motion which we need and
introduce the Ornstein-Uhlenbeck process with catalyst given by a superprocess.
The main results are the affine characterization of the characteristic
functional-Laplace transform of the joint catalytic O-U process and catalyst
process and the identification of basic properties of the quenched and annealed
versions of these processes.Comment: 23 page