Abstract
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.
Citation
John Verzani. "On the convex hull of planar Brownian snake." Ann. Probab. 24 (3) 1280 - 1299, July 1996. https://doi.org/10.1214/aop/1065725182
Information