Abstract
In this paper we consider a multilevel branching diffusion particle system and its diffusion approximation, which can be characterized as an $M(M(R^d))$-valued process. The long term behavior of the limiting process is studied. The main results are that if $d \leq 4$, then the two level $M(M(R^d))$-valued process suffers local extinction, and if $d = 4$, then the process has a self-similarity property.
Citation
Yadong Wu. "Asymptotic Behavior of the Two Level Measure Branching Process." Ann. Probab. 22 (2) 854 - 874, April, 1994. https://doi.org/10.1214/aop/1176988733
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