Concentration of the Brownian bridge on the hyperbolic plane

• 成果类型: Article
• 署名作者: Simon, T
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1977-1989
• 关键词: spaces

摘要

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 around 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.