The planar Brownian snake is a continuous, strong Markov process
taking values in the space of continuous functions in $\mathbb{R}^2$ that are
stopped at some time. For a fixed time the snake is distributed like a planar
Brownian motion with a random lifetime. This paper characterizes the convex
hull of the trace of the snake paths that exit the half-plane at the origin. It
is shown that the convex hull at 0 is roughly a factor of x smoother than the
convex hull of a piece of planar Brownian motion at its minimum y-value.
@article{1065725182,
author = {Verzani, John},
title = {On the convex hull of planar Brownian snake},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1280-1299},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725182}
}
Verzani, John. On the convex hull of planar Brownian snake. Ann. Probab., Tome 24 (1996) no. 2, pp. 1280-1299. http://gdmltest.u-ga.fr/item/1065725182/