Minimal thinness for subordinate Brownian motion in half-space

Minimal thinness for subordinate Brownian motion in half-space

— We study minimal thinness in the half-space H := {x = (x̃, xd) : x̃ ∈ Rd−1, xd > 0} for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of H below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy. Résumé. — Nous é...

Minimal thinness with respect to subordinate killed Brownian motions

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C domains, C domains with compact complements and domains above graphs of bounded C functions. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40; Secondary 31C35, 60J45, 60...

Potential Theory of Subordinate Brownian Motion

Harmonic functions of subordinate killed Brownian motion

In this paper we study harmonic functions of subordinate killed Brownian motion in a domain D: We first prove that, when the killed Brownian semigroup in D is intrinsic ultracontractive, all nonnegative harmonic functions of the subordinate killed Brownian motion in D are continuous and then we establish a Harnack inequality for these harmonic functions. We then show that, when D is a bounded L...

Potential Theory of Subordinate Killed Brownian Motion in a Domain∗

Abstract. Subordination of a killed Brownian motion in a bounded domain D ⊂ R via an α/2-stable subordinator gives a process Zt whose infinitesimal generator is −(− |D), the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process Zt in a Lipschitz domain D by comparing the process with the rotationally invariant α-stable process killed upon exi...