Ratio Limit Theorems for a Brownian Motion Killed at the Boundary of a Benedicks Domain
Pierre Collet, Servet Martı́nez, Jaime San Martı́n · The Annals of Probability · 1999
We consider a Brownian motion in a Benedicks domain with absorption at the boundary. We show ratio limit theorems for the associated heat kernel. When the hole is compact, therefore the Martin boundary is two dimensional; we obtain sharp estimates on the lifetime probabilities and we identify, in probabilistic terms, the various constants appearing in the theory.