On the asymptotic behavior of the hyperbolic Brownian motion

Abstract

The main results in this paper concern large and moderate deviations for the radial component of a $n$-dimensional hyperbolic Brownian motion (for $n\ge 2$) on the Poincaré half-space. We also investigate the asymptotic behavior of the hitting probability $P_{\eta }(T_{{\eta }_1}^{(n)}<\infty )$ of a ball of radius ${\eta }_1$, as the distance $\eta$ of the starting point of the hyperbolic Brownian motion goes to infinity.

References in corpus (3)

• Hyperbolic geometrical optics: Hyperbolic glass
• Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces
• Hitting spheres on hyperbolic spaces

Cited by in corpus (1)

• Cutoff on Hyperbolic Surfaces