Conditional Brownian Motion in Rapidly Exhaustible Domains
Conditional Brownian Motion in Rapidly Exhaustible Domains
Let $D$ be a domain in $\mathbb{R}^d$ and let $\Delta_1$ be the set of minimal points of the Martin boundary of $D$. For $x \in D$ and $z \in \Delta_1$, let $(X_t)$ under the law $P^{x; z}$ be Brownian motion in $D$, starting at $x$ and conditioned to converge to …