Sharp estimates of Green function of hyperbolic Brownian Motion
Kamil Bogus, Tomasz Byczkowski, Jacek Malecki
TL;DR
This paper derives precise two-sided estimates for the Green function of hyperbolic Brownian motion in a half-space, building on recent Bessel heat kernel estimates to enhance understanding of the process's potential theory.
Contribution
It provides sharp, two-sided estimates of the Green function for hyperbolic Brownian motion, extending existing results with new bounds based on recent Bessel heat kernel estimates.
Findings
Sharp two-sided estimates for the Green function
Enhanced understanding of hyperbolic Brownian motion
Application of recent Bessel heat kernel results
Abstract
The main objective of the work is to provide sharp two-sided estimates of -Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtained by K. Bogus and J. Malecki [3], regarding precise estimates of the Bessel heat kernel of half-lines.
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