Abstract.
Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C 1,1 open set D are obtained, where α (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.
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Received: 27 January 2002 / Revised version: 10 June 2002 / Published online: 24 October 2002
This research is supported in part by NSF Grant DMS-0071486.
Mathematics Subject Classification (2002): Primary: 60J45, 31C35; Secondary: 60G52, 31C15
Keywords or phrases: Censored stable process – Green function – Capacity – Martin boundary – Martin kernel – Harmonic function
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Chen, ZQ., Kim, P. Green function estimate for censored stable processes. Probab Theory Relat Fields 124, 595–610 (2002). https://doi.org/10.1007/s00440-002-0226-2
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DOI: https://doi.org/10.1007/s00440-002-0226-2