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- W1580455522 abstract "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." @default.
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- W1580455522 date "2006-02-01" @default.
- W1580455522 modified "2023-09-26" @default.
- W1580455522 title "Brownian motion in self-similar domains" @default.
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