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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 50 open journal systems 


Local extinction for superprocesses in random environments

Leonid Mytnik, Technion
Jie Xiong, University of Tennessee and Hebei Normal University


Abstract
We consider a superprocess in a random environment represented by a random measure which is white in time and colored in space with correlation kernel g(x,y). Suppose that g(x,y) decays at a rate of |x-y|-α, 0≤α≤ 2, as |x-y|->∞. We show that the process, starting from Lebesgue measure, suffers longterm local extinction. If α<2, then it even suffers finite time local extinction. This property is in contrast with the classical super-Brownian motion which has a non-trivial limit when the spatial dimension is higher than 2. We also show in this paper that in dimensions d=1,2 superprocess in random environment suffers local extinction for any bounded function g.


Full text: PDF

Pages: 1349-1378

Published on: November 3, 2007
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Electronic Journal of Probability. ISSN: 1083-6489