Synchronous couplings of reflected Brownian motions in smooth domains
Burdzy, Krzysztof ; Chen, Zhen-Qing ; Jones, Peter
Illinois J. Math., Tome 50 (2006) no. 1-4, p. 189-268 / Harvested from Project Euclid
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For every bounded planar domain $D$ with a smooth boundary, we define a ``Lyapunov exponent'' $\Lambda(D)$ 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 $\Lambda(D)>0$ then the distance between the two Brownian particles goes to $0$ exponentially fast with rate $\Lambda (D)/(2|D|)$ as time goes to infinity. The exponent $\Lambda(D)$ is strictly positive if the domain has at most one hole. It is an open problem whether there exists a domain with $\Lambda(D)<0$.
Publié le : 2006-05-15
Classification:  60J65 
@article{1258059475,
     author = {Burdzy, Krzysztof and Chen, Zhen-Qing and Jones, Peter},
     title = {Synchronous couplings of reflected Brownian motions in smooth domains},
     journal = {Illinois J. Math.},
     volume = {50},
     number = {1-4},
     year = {2006},
     pages = { 189-268},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258059475}
}

Burdzy, Krzysztof; Chen, Zhen-Qing; Jones, Peter. Synchronous couplings of reflected Brownian motions in smooth domains. Illinois J. Math., Tome 50 (2006) no. 1-4, pp.  189-268. http://gdmltest.u-ga.fr/item/1258059475/