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January, 1988 On the Supports of Measure-Valued Critical Branching Brownian Motion
I. Iscoe
Ann. Probab. 16(1): 200-221 (January, 1988). DOI: 10.1214/aop/1176991895


Let $(X_t)_{t \geq 0}$ denote the measure-valued critical branching Brownian motion. When the support of the initial state, $X_0$, is bounded, temporally global results are given concerning the range, i.e., the size of the supports of $(X_t)_{t \geq 0}$, and the hitting (i.e., charging) probabilities of distant balls are evaluated asymptotically; they depend strongly on the dimension, $d$, of the underlying Euclidean space $\mathbb{R}^d$. In contrast, in the case $d = 1$ and $X_0 = \lambda$ (Lebesgue measure), it is shown that (spatially) local extinction occurs. Also extensions are indicated for the case of an infinite variance branching mechanism; these results are also dimensionally dependent.


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I. Iscoe. "On the Supports of Measure-Valued Critical Branching Brownian Motion." Ann. Probab. 16 (1) 200 - 221, January, 1988.


Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0635.60094
MathSciNet: MR920265
Digital Object Identifier: 10.1214/aop/1176991895

Primary: 60G57
Secondary: 34B15 , 60J80

Keywords: asymptotics , hitting probability , Local extinction , Measure-valued branching diffusion , ‎range‎ , singular elliptic boundary value problems , Support

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • January, 1988
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