Concentration of the Brownian bridge on the hyperbolic plane
Thomas Simon
Source: Ann. Probab. Volume 30, Number 4
(2002), 1977-1989.
Abstract
We consider a Brownian bridge on the hyperbolic plane with one extremity tending to infinity, in finite time. We show that the exact exponential rate according to which this process concentrates round the geodesical segment joining the origin o to the moving extremity z is $-\rho(o,z)$, where $\rho$ stands for the hyperbolic distance. This improves a result of A. Eberle.
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Keywords: Brownian bridge; first passage times; geodesics; $h$-transform; hyperbolic plane; special functions
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1039548379
Digital Object Identifier: doi:10.1214/aop/1039548379
Mathematical Reviews number (MathSciNet): MR1944013
Zentralblatt MATH identifier: 1018.60080
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