An invariance principle for branching diffusions in bounded domains
成果类型：
Article
署名作者：
Powell, Ellen
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0847-8
发表日期：
2019
页码：
999-1062
关键词：
摘要：
We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary D. It is known that any such process undergoes a phase transition when the branching rate exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under appropriate rescaling. The result holds under only a mild assumption on the domain, and is valid for all branching mechanisms with finite variance, and a general class of diffusions.
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