On the convex hull of planar Brownian snake

• 成果类型: Article
• 署名作者: Verzani, J
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1065725182
• 发表日期: 1996
• 页码: 1280-1299
• 关键词: motion

摘要

The planar Brownian snake is a continuous, strong Markov process taking values in the space of continuous functions in 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.