Year: 2011
Type: preprint
Abstract: Let X^μ={X_t^μ;t>=0}, μ>0, be the n-dimensional hyperbolic Brownian motion with drift, that is a diffusion on the real hyperbolic space H^n having the Laplace-Beltrami operator with drift as its generator. We prove the reflection principle for X^μ, which enables us to study the process X^μkilled when exiting the hyperbolic half-space, that is the set D={x\in H^n: x_1>0}. We provide formulae, uniform estimates and describe asymptotic behavior of the Green function and the Poisson kernel of D for the process X^μ. Finally, we derive formula for the lambda-Poisson kernel of the set D.
Source: arXiv (Cornell University)
Authors: Malecki, Jacek, Serafin, Grzegorz
Institution: Wrocław University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1630336573