Synchronous couplings of reflected Brownian motions in smooth domains
| dc.creator | Burdzy, Krzysztof | |
| dc.creator | Chen, Zhen-Qing | |
| dc.creator | Jones, Peter | |
| dc.date | 2005-01-27 | |
| dc.date.accessioned | 2026-07-07T05:16:27Z | |
| dc.date.available | 2026-07-07T05:16:27Z | |
| dc.description | For every bounded planar domain $D$ with a smooth boundary, we define a `Lyapunov exponent' $Λ(D)$ using a fairly explicit formula. We consider two reflected Brownian motions in $D$, driven by the same Brownian motion (i.e., a `synchronous coupling'). If $Λ(D)>0$ then the distance between the two Brownian particles goes to 0 exponentially fast with rate $Λ(D)/(2|D|)$ as time goes to infinity. The exponent $Λ(D)$ is strictly positive if the domain has at most one hole. It is an open problem whether there exists a domain with $Λ(D)<0$. | |
| dc.identifier | https://arxiv.org/abs/math/0501486 | |
| dc.identifier | http://arxiv.org/abs/math/0501486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73993 | |
| dc.subject | Probability | |
| dc.subject | 60J65; 60J55 | |
| dc.title | Synchronous couplings of reflected Brownian motions in smooth domains | |
| dc.type | text |