Patterns in Random Walks and Brownian Motion

被引：2

作者：

Pitman, Jim ^{[1
]}

Tang, Wenpin ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, 367 Evans Hall, Berkeley, CA 94720 USA

来源：

IN MEMORIAM MARC YOR - SEMINAIRE DE PROBABILITES XLVII | 2015年 / 2137卷

关键词：

POTENTIAL-THEORY; PATH DECOMPOSITION; LEVY PROCESSES; RANDOM TREE; LOCAL TIME; CAPACITY; EXCURSIONS; RANGE; SETS;

D O I：

10.1007/978-3-319-18585-9_4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.

引用

页码：49 / 88

页数：40