Hitting Times of Points and Intervals for Symmetric Lévy Processes

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Abstract

For one-dimensional symmetric Lévy processes, which hit every point with positive probability, we give sharp bounds for the tail function Px(TB>t), where TB 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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Grzywny, T., & Ryznar, M. (2017). Hitting Times of Points and Intervals for Symmetric Lévy Processes. Potential Analysis, 46(4), 739–777. https://doi.org/10.1007/s11118-016-9600-z

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