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October 2002 Concentration of the Brownian bridge on the hyperbolic plane
Thomas Simon
Ann. Probab. 30(4): 1977-1989 (October 2002). DOI: 10.1214/aop/1039548379

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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Thomas Simon. "Concentration of the Brownian bridge on the hyperbolic plane." Ann. Probab. 30 (4) 1977 - 1989, October 2002. https://doi.org/10.1214/aop/1039548379

Information

Published: October 2002
First available in Project Euclid: 10 December 2002

zbMATH: 1018.60080
MathSciNet: MR1944013
Digital Object Identifier: 10.1214/aop/1039548379

Subjects:
Primary: 58J65
Secondary: 60J60

Keywords: $h$-transform , Brownian bridge , first passage times , geodesics , hyperbolic plane , Special functions

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 4 • October 2002
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