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

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  • Engländer, János

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.

Suggested Citation

  • Engländer, János, 2000. "On the volume of the supercritical super-Brownian sausage conditioned on survival," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 225-243, August.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:2:p:225-243
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    References listed on IDEAS

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    1. Tribe, Roger, 1994. "A representation for super Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 51(2), pages 207-219, July.
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