Central Limit Theorems for the Single Point Catalytic Super-Brownian Motion with Immigration

Abstract

We establish the central limit theorems for the single point catalytic super- Brownian motion with deterministic immigration and single point catalytic super- Brownian motion immigration on the Schwartz space and a weighted Sobolev space. For the catalytic immigration case, the weak convergence depends on the branching rates of both immigration part and non-immigration part.