## The Annals of Probability

### On the convex hull of planar Brownian snake

John Verzani

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 9 October 2003

https://projecteuclid.org/euclid.aop/1065725182

Digital Object Identifier
doi:10.1214/aop/1065725182

Mathematical Reviews number (MathSciNet)
MR1411495

Zentralblatt MATH identifier
0862.60028

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

#### Citation

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