| Título: | Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion |
| Autores: |
Abraham, Romain; Université René Descartes (Paris 5) Werner, Wendelin; Université Paris-Sud and IUF |
| Fecha: | 1997-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Brownian snakes, superprocesses, non-linear differential equations 60J25, 60J45 |
| Descripción: | We investigate the asymptotic behaviour of the probability that a normalized $d$-dimensional Brownian snake (for instance when the life-time process is an excursion of height 1) avoids 0 when starting at distance $\varepsilon$ from the origin. In particular we show that when $\varepsilon$ tends to 0, this probability respectively behaves (up to multiplicative constants) like $\varepsilon^4$, $\varepsilon^{2\sqrt{2}}$ and $\varepsilon^{(\sqrt {17}-1)/2}$, when $d=1$, $d=2$ and $d=3$. Analogous results are derived for super-Brownian motion started from $\delta_x$ (conditioned to survive until some time) when the modulus of $x$ tends to 0. |
| Idioma: | No aplica |
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