A quasimode expansion in powers of 1/|ln epsilon| yields rigorous asymptotics for the mean exit time and per-window exit probabilities of reflected Brownian motion in a 2D domain with small boundary holes.
Br´ ezis,Functional analysis, sobolev spaces and partial differential equations, Vol
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A spectral approach to the narrow escape problem in two-dimensional domains
A quasimode expansion in powers of 1/|ln epsilon| yields rigorous asymptotics for the mean exit time and per-window exit probabilities of reflected Brownian motion in a 2D domain with small boundary holes.