 Planar Brownian annulus hitting probability

ID: planar-brownian-annulus-hitting-probability

x

with

0 < r < ∣ x ∣ < R

P_{x} (T_{r} < T_{R}) = \frac{l o g R - l o g ∣ x ∣}{l o g R - l o g r} .

This is optional stopping applied to the harmonic function

lo g ∣ x ∣

on the annulus.

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