Potential Analysis

, Volume 25, Issue 4, pp 371–386 | Cite as

Symmetric Stable Processes on Unbounded Domains



Let \(X_{\,t}\) be a symmetric \(\alpha\)-stable process in \(\mathbb{R}^{d}\), \(d\geq2\), \(\alpha\in(0,2)\). We give necessary and sufficient condition under which the expectation of a very general function of the exit time from horns is finite. These domains include the symmetric domains given by increasing functions studied earlier by various authors. Our methods differ from those in earlier papers in that we obtain our results from estimates on the transition densities instead of harmonic measure. Some of this estimates are of independent interest.

Key words

symmetric stable process horn-shaped domains exit time heat kernel 

Mathematics Subject Classifications (2000)

31B05 60J45 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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