Harmonic measures for symmetric stable processes

• Autorzy: Jang-Mei Wu
• Języki publikacji: EN

Abstrakty

EN

Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on $D^{c}$ with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and $D^{c}∖S$ that determine whether ω(S,D) is zero or positive.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 3
• Strony: 279-291

Daty

wydano

2002

Twórcy

autor

Jang-Mei Wu

• Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/sm149-3-5