Cutting Brownian Paths
Author： Richard F. Bass;Krzysztof Burdzy
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470402464
P-ISBN(Paperback): 9780821809686
P-ISBN(Hardback): 9780821809686
Subject： O211.6 stochastic process
Keyword： Probability and Statistics
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Cutting Brownian Paths
Description
A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? Let $Z_t$ be two-dimensional Brownian motion. Say that a straight line $\mathcal L$ is a cut line if there exists a time $t \in (0,1)$ such that the trace of $\{ Z_s: 0 \leq s < t\}$ lies on one side of $\mathcal L$ and the trace of $\{Z_s: t < s < 1\}$ lies on the other side of $\mathcal L$. In this volume, the authors provide a solution, discuss related works, and present a number of open problems.