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July 1996 On the convex hull of planar Brownian snake
John Verzani
Ann. Probab. 24(3): 1280-1299 (July 1996). DOI: 10.1214/aop/1065725182


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.


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John Verzani. "On the convex hull of planar Brownian snake." Ann. Probab. 24 (3) 1280 - 1299, July 1996.


Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0862.60028
MathSciNet: MR1411495
Digital Object Identifier: 10.1214/aop/1065725182

Primary: 60G17
Secondary: 60J80

Keywords: Brownian snake , Convex hull , path-valued process

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 3 • July 1996
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