Abstract
For , the domain G is T-homogeneous if TG=G. If , then necessarily . It is known that for some p>0, the Martin kernel K at infinity satisfies for all . We show that in dimension , if G is also Lipschitz, then the exit time τG of Brownian motion from G satisfies as . An analogous result holds for conditioned Brownian motion, but this time the decay power is . In two dimensions, we can relax the Lipschitz condition at 0 at the expense of making the rest of the boundary C2.
Citation
Dante Deblassie. Robert Smits. "Brownian motion in self-similar domains." Bernoulli 12 (1) 113 - 132, February 2006.
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