On the laws of first hitting times of points for one-dimensional symmetric stable L\'evy processes

TL;DR

This paper investigates the probabilistic laws governing the first hitting times of points by one-dimensional symmetric stable Lévy processes, utilizing Ito's excursion theory to deepen understanding of these stochastic phenomena.

Contribution

It introduces new insights into the laws of first hitting times for symmetric stable Lévy processes using excursion theory, advancing theoretical understanding in stochastic processes.

Findings

Derived explicit laws for first hitting times of points.

Applied excursion theory to analyze hitting time distributions.

Enhanced theoretical framework for symmetric stable Lévy processes.

Abstract

Several aspects of the laws of first hitting times of points are investigated for one-dimensional symmetric stable L\'evy processes. It\^o's excursion theory plays a key role in this study.