Abstract
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.
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Supported in part by NSF grant #9700585-DMS and RTN Harmonic Analysis and Related Problems contract HPRN-CT-2001-00273-HARP.
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Siudeja, B. Symmetric Stable Processes on Unbounded Domains. Potential Anal 25, 371–386 (2006). https://doi.org/10.1007/s11118-006-9022-4
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DOI: https://doi.org/10.1007/s11118-006-9022-4