Potential theory of subordinate killed Brownian motion

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...

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 Brownian Motions Revisited

The paper discusses and surveys some aspects of the potential theory of subordinate Brownian motion under the assumption that the Laplace exponent of the corresponding subordinator is comparable to a regularly varying function at infinity. This extends some results previously obtained under stronger conditions. AMS 2010 Mathematics Subject Classification: Primary 60J45 Secondary 60G51, 60J35, 6...

Potential Theory of Special Subordinators and Subordinate Killed Stable Processes

In this paper we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open set D with special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable p...