Abstract
In this paper we address the question of finding the point which maximizes the pth moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method for excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.
| Original language | English |
|---|---|
| Pages (from-to) | 1135-1149 |
| Number of pages | 15 |
| Journal | Journal of Applied Probability |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2020 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Applied Probability Trust 2020.
Keywords
- Planar Brownian motion
- exit time
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty