Potential Theory of Special Subordinators and Subordinate Killed Stable Processes

Renming Song () and Zoran Vondraček ()
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Renming Song: University of Illinois
Zoran Vondraček: University of Zagreb

Journal of Theoretical Probability, 2006, vol. 19, issue 4, 817-847

Abstract: 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 process and the nonnegative harmonic functions of the subordinate killed symmetric stable process. We show that nonnegative harmonic functions of the subordinate killed symmetric stable process are continuous and satisfy a Harnack inequality. We then show that, when D is a bounded κ-fat set, both the Martin boundary and the minimal Martin boundary of the subordinate killed symmetric stable process in D coincide with the Euclidean boundary ∂D.

Keywords: Killed Brownian motions; killed symmetric stable processes; subordinators; Bernstein functions; complete Bernstein functions; subordination; harmonic functions; Green function; Martin kernel; Martin boundary; Harnack inequality; Primary 60J45; Secondary 60J75; Secondary 31C05; Secondary 31C35 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-006-0045-y

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