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

Zenghu Li; Jie Xiong

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arXiv · 0802.0926

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

Zenghu Li·Jie Xiong

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Abstract

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 (2003). As an application of the stochastic equation, it is proved that the superprocess possesses a local time which is Holder 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.

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Zenghu Li, Jie Xiong. 2008-02-07. Continuous local time of a purely atomic immigration superprocess with dependent spatial motion. https://arxiv.org/abs/0802.0926

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