在实际线上，lsamvy过程的命中概率

Pub Date : 2021-01-01 DOI:10.30757/ALEA.V18-27

T. Grzywny, Łukasz Leżaj, Maciej Miśta

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引用次数: 3

摘要

对于满足积分条件∫∞0 dξ 1 + Reψ(ξ) <∞的一般非对称过程，证明了有界区间第一次命中时间的尾概率的尖锐双边估计及其渐近性。为此，我们首先证明并应用了全局尺度不变的哈纳克不等式。在一定条件下得到了特征指数的结果。我们提供了一系列满足这些假设的lsamvy过程。

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Hitting probabilities for Lévy processes on the real line

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 ∫ ∞ 0 dξ 1 + Reψ(ξ) < ∞. 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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