| Título: | Local extinction for superprocesses in random environments |
| Autores: |
Mytnik, Leonid; Technion Xiong, Jie; University of Tennessee and Hebei Normal University |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: | No aplica |
| Descripción: | 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 $|x-y|^{-\alpha}$, $0\leq \alpha\leq 2$, as $|x-y|\to\infty$. We show that the process, starting from Lebesgue measure, suffers longterm local extinction. If $\alpha < 2$, 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 $g$. |
| Idioma: | No aplica |
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