Censored stable processes

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Censored stable processes

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Title: Censored stable processes
Author: Burdzy, Krzysztof; Bogdan, Krzysztof; Chen, Zhen-Qing
Abstract: We present several constructions of a "censored stable process" in an open set D [is an element of the subset] R [to the power of] n, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time—we give sharp conditions for such approach in terms of the stability index [alpha] and the "thickness" of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent case. We also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary. We derive a boundary Harnack principle in C [to the power of] 1,1 open sets.
URI: http://hdl.handle.net/1773/2221

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