Xiong, Jie; Zhou, Xiaowen Superprocess over a stochastic flow with superprocess catalyst. (English) Zbl 1063.60123 Int. J. Pure Appl. Math. 17, No. 3, 353-382 (2004). Summary: We study the catalytic superprocesses under a stochastic flow where the catalyst itself is a superprocess under the same flow. Comparing with the study of the superprocess under a stochastic flow with deterministic catalyst, here we encounter a serious adaptability problem caused by this common stochastic flow in proving the uniqueness by using the usual conditional log-Laplace transform approach. To overcome this difficulty, we find a limiting moment dual and show that the moments increase not too fast so that the moments determine the distribution. We also prove the state property by the moment method. Cited in 3 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:catalytic superprocesses; random medium; branching particle system PDFBibTeX XMLCite \textit{J. Xiong} and \textit{X. Zhou}, Int. J. Pure Appl. Math. 17, No. 3, 353--382 (2004; Zbl 1063.60123)