The Annals of Probability

On the convex hull of planar Brownian snake

John Verzani

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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 information

Ann. Probab., Volume 24, Number 3 (1996), 1280-1299.

First available in Project Euclid: 9 October 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G17: Sample path properties
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Convex hull Brownian snake path-valued process


Verzani, John. On the convex hull of planar Brownian snake. Ann. Probab. 24 (1996), no. 3, 1280--1299. doi:10.1214/aop/1065725182.

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