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February 2006 Brownian motion in self-similar domains
Dante Deblassie, Robert Smits
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Bernoulli 12(1): 113-132 (February 2006).


For T 1 , the domain G is T-homogeneous if TG=G. If 0 ¬G , then necessarily 0 G . It is known that for some p>0, the Martin kernel K at infinity satisfies K (Tx)=T pK(x) for all x G . We show that in dimension d 2 , if G is also Lipschitz, then the exit time τG of Brownian motion from G satisfies P x (τ G>t)K(x)t - p/2 as t . An analogous result holds for conditioned Brownian motion, but this time the decay power is 1 -p-d/2 . In two dimensions, we can relax the Lipschitz condition at 0 at the expense of making the rest of the boundary C2.


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Dante Deblassie. Robert Smits. "Brownian motion in self-similar domains." Bernoulli 12 (1) 113 - 132, February 2006.


Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1101.60062
MathSciNet: MR2202324

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 1 • February 2006
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