On the volume of the supercritical super-Brownian sausage conditioned on survival

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:88

Article

Engländer, J

关键词: super-Brownian motion;    super-sausage;    branching Brownian motion;    Poissonian traps;    hard obstacles;   

DOI  :  10.1016/S0304-4149(00)00003-X

来源: Elsevier

【 摘 要 】

Let alpha and beta be positive constants. Let X be the supercritical super-Brownian motion corresponding to the evolution equation u(t) = 1/2 Delta + beta u - alpha u(2) in R-d and let Z be the binary branching Brownian-motion with branching rate beta. For t greater than or equal to 0, let R(t) = boolean ORs=0t supp(X(s)), that is R(t) is the (accumulated) support of X up to time t. For t greater than or equal to 0 and a > 0, let R-a(t) = boolean ORx is an element of R(t) (B) over bar(x,a). We call R-a(t) the super-Brownian sausage corresponding to the supercritical super-Brownian motion X. For t greater than or equal to 0, let (R) over cap(t) = boolean ORs=0t supp(Z(s)), that is (R) over cap(t) is the (accumulated) support of Z up to time t. For t greater than or equal to 0 and a > 0, let (R) over cap(a)(t) = boolean ORx is an element of R(t) (B) over bar(x,a). We call (R) over cap(a)(t) the branching Brownian sausage corresponding to Z. In this paper we prove that [GRAPHICS] [GRAPHICS] for all d greater than or equal to 2 and all a, alpha, v > 0. (c) 2000 Elsevier Science B.V. All rights reserved.

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