Patterns in random walks and Brownian motion
Probability
2015-09-18 v3
Abstract
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.
Cite
@article{arxiv.1411.0041,
title = {Patterns in random walks and Brownian motion},
author = {Jim Pitman and Wenpin Tang},
journal= {arXiv preprint arXiv:1411.0041},
year = {2015}
}
Comments
31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_4