Continuous local time of a purely atomic immigration superprocess with dependent spatial motion

A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law of a Feller branching diffusion, which generalizes the work of Dawson and Li [3]. As an application of the stochastic equation, it is proved that the superprocess possesses a local time which is Hölder continuous of order α for every α < 1/2. We establish two scaling limit theorems for the immigration superprocess, from which we derive scaling limits for the corresponding local time.