Abstract
For one-dimensional symmetric Lévy processes, which hit every point with positive probability, we give sharp bounds for the tail function Px(T B >t), where T B is the first hitting time of B which is either a single point or an interval. The estimates are obtained under some weak type scaling assumptions on the characteristic exponent of the process. We apply these results to prove sharp two-sided estimates of the transition density of the process killed after hitting B.
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The research was supported in part by the National Science Centre (Poland): grant 2014/14/M/ST1/00600
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Grzywny, T., Ryznar, M. Hitting Times of Points and Intervals for Symmetric Lévy Processes. Potential Anal 46, 739–777 (2017). https://doi.org/10.1007/s11118-016-9600-z
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DOI: https://doi.org/10.1007/s11118-016-9600-z