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

János Engländer

Stochastic Processes and their Applications, 2000, vol. 88, issue 2, 225-243

Abstract: Let [alpha] and [beta] be positive constants. Let X be the supercritical super-Brownian motion corresponding to the evolution equation in and let Z be the binary branching Brownian-motion with branching rate [beta]. For t[greater-or-equal, slanted]0, let , that is R(t) is the (accumulated) support of X up to time t. For t[greater-or-equal, slanted]0 and a>0, let We call Ra(t) the super-Brownian sausage corresponding to the supercritical super-Brownian motion X. For t[greater-or-equal, slanted]0, let , that is is the (accumulated) support of Z up to time t. For t[greater-or-equal, slanted]0 and a>0, let We call the branching Brownian sausage corresponding to Z. In this paper we prove that for all d[greater-or-equal, slanted]2 and all a,[alpha],[nu]>0.

Keywords: Super-Brownian; motion; Super-sausage; Branching; Brownian; motion; Poissonian; traps; Hard; obstacles (search for similar items in EconPapers)
Date: 2000
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