Harmonic functions of subordinate killed Brownian motion

Abstract

Journal of Functional Analysis 215 (2004) 399-426. doi:10.1016/j.jfa.2004.01.001Received by publisher: 2003-09-12Harvest Date: 2016-01-04 12:20:11DOI: 10.1016/j.jfa.2004.01.001Page Range: 399-42

Potential Theory of Special Subordinators and Subordinate Killed Stable Processes

“…The resulting class of subordinate processes is a significant extension of the one studied in Ref. 15. In particular, this class contains discontinuous processes with a continuous component.…”

“…16 as Theorem 2 for the case of stable subordinators and used in Ref. 15. However, the proof given in Ref.…”

“…16 and Ref. 15, is the fact that stable subordinators are special. We will show in this paper that the main results of Ref.…”

“…16 and Ref. 15, remain valid for the killed Brownian motion X D subordinate by a special subordinator with infinite Lévy measure or positive drift (or both). The resulting class of subordinate processes is a significant extension of the one studied in Ref.…”

On the subordinate killed B.M in bounded domains and existence results for nonlinear fractional Dirichlet problems

“…This process was first studied in [7], where among other things, an one to one correspondence between the family of positive harmonic functions of the killed Brownian motion χ D and the family of positive harmonic functions of the subordinate killed Brownian motion Z D α was established. This correspondence was improved later in [6]. In particular, it was shown in [6], that there are no non-trivial bounded harmonic functions for Z D α .…”