Recurrence and transience of branching diffusion processes on Riemannian manifolds
成果类型：
Article
署名作者：
Grigor'yan, A; Kelbert, M
署名单位：
Imperial College London; Swansea University; Russian Academy of Sciences; Institute of Earthquake Prediction Theory & Mathematical Geophysics
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2003
页码：
244-284
关键词：
摘要：
We relate the recurrence and transience of a branching diffusion process on a Riemannian manifold M to some properties of a linear elliptic operator on M (including spectral properties). There is a trade-off between the tendency of the transient Brownian motion to escape and the birth process of the new particles. If the latter has a high enough intensity then it may override the transience of the Brownian motion, leading to the recurrence of the branching process, and vice versa. In the case of a spherically symmetric manifold, the critical intensity of the population growth can be found explicitly.