Limit theorems for the weighted occupation time for super-Brownian motions on H~d

摘要

Weighted occupation time processes associated with the super-Brownian motions on hyperbolic spaces are investigated. Longtime behavior and a central limit type theorem for the processes are obtained. For all dimension d >= 2, the right normings for two fluctuations are t and t , and the limit results are the Riemannian measure and some centered Gaussian random measure, respectively.