Continuous Local Time of a Purely Atomic Immigration Superprocess with Dependent Spatial Motion |
| |
| Authors: | Zenghu Li Jie Xiong |
| |
| Institution: | 1. School of Mathematical Sciences , Beijing Normal University , Beijing, P.R. China lizh@bnu.edu.cn;3. Department of Mathematics , University of Tennessee , Knoxville, Tennessee, USA;4. Department of Mathematics , Hebei Normal University , Shijiazhuang, P.R. China |
| |
| Abstract: | 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 3
Dawson , D.A. , and
Li , Z.H. 2003 . Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions . Probability Theory and Related Fields 127 : 37 – 61 . Google Scholar]]. 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. |
| |
| Keywords: | Dependent spatial motion Excursion Immigration Local time Poisson random measure Scaling limit theorem Superprocess |
|
|
