Hitting probabilities for Lévy processes on the real line

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-01-01 DOI:10.30757/ALEA.V18-27

T. Grzywny, Łukasz Leżaj, Maciej Miśta

引用次数: 3

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 ∫ ∞ 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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在实际线上，lsamvy过程的命中概率

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.