Burdzy, KrzysztofBogdan, KrzysztofChen, Zhen-Qing2005-11-302005-11-302003-09Bogdan, K., K. Burdzy, & Z.Q. Chen. (2003). Censored stable processes. Probability Theory and Related Fields, 127(1), 89-152.http://hdl.handle.net/1773/2221We 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.505122 bytesapplication/pdfen-USstable processboundaryBesov spacesHarnack principleArticle