Immigration process in catalytic medium (Q1974206)

Catalytic super-Brownian motion is a measure-valued process which is obtained as a limit of a rescaled system of branching Brownian motions where the branching occurs only in the presence of a catalyst [see, e.g., \textit{A. Klenke}, in the paper reviewed below for a recent review of the subject]. On the other hand, superprocesses with immigration have also been investigated recently [e.g. \textit{Z. Li}, Stochastic Processes Appl. 62, No. 1, 73-86 (1996; Zbl 0847.60071)]. The authors obtain a long time law of large numbers for dimensions \(d\leq 3\) and a central limit theorem for \(d= 3\), for an immigration process associated with catalytic super-Brownian motion and for its occupation time process, when the catalytic medium is determined by another super-Brownian motion.