Potential theory of hyperbolic Brownian motion in tube domains
Potential theory of hyperbolic Brownian motion in tube domains
Let $X=\{X(t);\,t\geq 0\}$ be the hyperbolic Brownian motion on the real hyperbolic space $\mathbb H^n=\{x\in \mathbb R^n:x_n>0\}$. We study the Green function and the Poisson kernel of tube domains of the form $D\times (0,\infty )\subset \mathbb H^n$, wh