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arXiv · 1911.05149

Hitting probabilities for Lévy processes on the real line

Tomasz Grzywny·Łukasz Leżaj·Maciej Miśta
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Abstract

We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty} \frac{dξ}{1+\operatorname{Re} ψ(ξ)}<\infty. \] To this end, we first prove and then apply the global scale invariant Harnack inequality. Results are obtained under certain conditions on the characteristic exponent. We provide a wide class of Lévy processs which satisfy these assumptions.

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Tomasz Grzywny, Łukasz Leżaj, Maciej Miśta. 2019-11-14. Hitting probabilities for Lévy processes on the real line. https://arxiv.org/abs/1911.05149

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