Conditions for a L\'evy process to stay positive near 0, in probability

TL;DR

This paper establishes a precise criterion based on the characteristics of a Lévy process that determines when it remains positive with high probability near zero, contributing to the understanding of its local behavior.

Contribution

It provides a necessary and sufficient condition for a Lévy process to stay positive near zero, linking this property to the process's defining characteristics.

Findings

Characterizes positivity near zero in terms of Lévy process parameters

Provides a criterion useful for Chung-type laws near zero

Enhances understanding of local path behavior of Lévy processes

Abstract

A necessary and sufficient condition for a L\'evy process $X$ to stay positive, in probability, near 0, which arises in studies of Chung-type laws for $X$ near 0, is given in terms of the characteristics of $X$.