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January 2003 Recurrence and transience of branching diffusion processes on Riemannian manifolds
Alexander Grigor'yan, Mark Kelbert
Ann. Probab. 31(1): 244-284 (January 2003). DOI: 10.1214/aop/1046294311


We relate the recurrence and transience of a branching diffusion process on a Riemannian manifold M to some properties of a linear elliptic operator onM (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.


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Alexander Grigor'yan. Mark Kelbert. "Recurrence and transience of branching diffusion processes on Riemannian manifolds." Ann. Probab. 31 (1) 244 - 284, January 2003.


Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1014.60081
MathSciNet: MR1959793
Digital Object Identifier: 10.1214/aop/1046294311

Primary: 58J65 , 60J80

Keywords: branching process , Brownian motion , gauge , maximum principle , recurrence , Riemannian manifold , transience

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 1 • January 2003
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