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


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.


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Romain Abraham. Wendelin Werner. "Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion." Electron. J. Probab. 2 1 - 27, 1997.


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

Primary: 60J25
Secondary: 60J45

Keywords: Brownian snakes , non-linear differential equations , Superprocesses

Vol.2 • 1997
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