Translator Disclaimer
1997 Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion
Romain Abraham, Wendelin Werner
Author Affiliations +
Electron. J. Probab. 2: 1-27 (1997). DOI: 10.1214/EJP.v2-17

Abstract

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.

Citation

Download Citation

Romain Abraham. Wendelin Werner. "Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion." Electron. J. Probab. 2 1 - 27, 1997. https://doi.org/10.1214/EJP.v2-17

Information

Accepted: 7 May 1997; Published: 1997
First available in Project Euclid: 26 January 2016

zbMATH: 0890.60068
MathSciNet: MR1447333
Digital Object Identifier: 10.1214/EJP.v2-17

Subjects:
Primary: 60J25
Secondary: 60J45

JOURNAL ARTICLE
27 PAGES


SHARE
Vol.2 • 1997
Back to Top