Potential Theory of Truncated Stable Processes

Details Potential Theory of Truncated Stable Processes Potential Theory of Truncated Stable Processes

2006-05-18

arxiv.org/abs/math/0605533v3

Mathematics

Probability

35 page, to appear in Mathematische Zeitschrift

Scientific paper

For any 0 < alpha <2, a truncated symmetric alpha-stable process is a symmetric Levy process in R^d with a Levy density given by c|x|^{-d-alpha} 1_{|x|< 1} for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic nonnegative functions these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails.

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