RECURRENCE AND TRANSIENCE OF BRANCHING DIFFUSION PROCESSES ON RIEMANNIAN MANIFOLDS
RECURRENCE AND TRANSIENCE OF BRANCHING DIFFUSION PROCESSES ON RIEMANNIAN MANIFOLDS
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黎曼流形上的支化扩散过程的反复性和瞬态性
DOI：
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发表时间：
2003
期刊：
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通讯作者：
M. Kelbert
中科院分区：
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作者：
A. Grigor’yan;M. Kelbert
将黎曼流形M上分支扩散过程的递归性和暂态性与M上的线性椭圆算子的一些性质（包括谱性质）联系起来。在瞬态布朗运动逃逸的趋势和新粒子的产生过程之间存在着一种权衡。如果后者具有足够高的强度，那么它可能会覆盖布朗运动的瞬态，导致分支过程的复发，反之亦然。对于球对称流形，可以明确地求出种群增长的临界强度。
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.