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Kelvin transform for (…)-harmonic functions in regular domains

Michalik K., Ryznar M.

Demonstratio Mathematica

2012

Vol. 45, nr 2

361-376

We investigate conditional stable processes in a Lipschitz domain D and conditional stable processes in the image of D under the Kelvin transform. We show that, with a suitable change of time, these processes are equal in distribution. As an application, we show the equivalence of the Hardy spaces and the relative Fatou theorem for D and its image.

The estimates for the Green Function in Lipschitz domains for the symmetric stable processes

Jakubowski T.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

419--441

We give sharp global estimates for the Green function, Martin kernel and Poisson kernel in Lipschitz domains for symmetric α-stable processes. We give some applications of the estimates.

On harmonic measure for Lévy processes

Sztonyk P.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 2

383--390

Let {Xt} be a Lévy process in Rd, d ≥ 2, with infinite Lévy measure. If {Xt} has no Gaussian component, then the process does not hit the boundary of Lipschitz domain S ⊂ Rd at the first exit time of S under mild conditions on {Xt}. The conditions are met, e.g., if {Xt} is rotation invariant.