On the Potential Theory of One-dimensional Subordinate Brownian Motions with Continuous Components |
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| Authors: | Panki Kim Renming Song Zoran Vondraček |
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| Institution: | 1.Department of Mathematics and Research Institute of Mathematics,Seoul National University,Seoul,Republic of Korea;2.Department of Mathematics,University of Illinois,Urbana,USA;3.Department of Mathematics,University of Zagreb,Zagreb,Croatia |
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| Abstract: | Suppose that S is a subordinator with a nonzero drift and W is an independent 1-dimensional Brownian motion. We study the subordinate Brownian motion X defined by X
t
= W(S
t
). We give sharp bounds for the Green function of the process X killed upon exiting a bounded open interval and prove a boundary Harnack principle. In the case when S is a stable subordinator with a positive drift, we prove sharp bounds for the Green function of X in (0, ∞ ), and sharp bounds for the Poisson kernel of X in a bounded open interval. |
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