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Continuous local time of a purely atomic immigration superprocess with dependent spatial motion. (English) Zbl 1128.60073

Summary: 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 D. A. Dawson and Z. Li [Probab. Theory Relat. Fields 127, No. 1, 37–61 (2003; Zbl 1038.60082)]. As an application of the stochastic equation, it is proved that the superprocess possesses a local time which is Hölder continuous of order \(\alpha \) for every \( \alpha < 1/2\). We establish two scaling limit theorems for the immigration superprocess, from which we derive scaling limits for the corresponding local time.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G57 Random measures
60H20 Stochastic integral equations

Citations:

Zbl 1038.60082
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References:

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