@article{EJP17,
author = {Romain Abraham and Wendelin Werner},
title = {Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {2},
year = {1997},
keywords = {Brownian snakes, superprocesses, non-linear differential equations},
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.},
pages = {no. 3, 1-27},
issn = {1083-6489},
doi = {10.1214/EJP.v2-17},
url = {http://ejp.ejpecp.org/article/view/17}}