Inverse local time of one-dimensional diffusions and its comparison theorem

TL;DR

This paper investigates the inverse local time of one-dimensional reflected diffusions, establishing a comparison principle and applying it to Green function estimates for non-local operators.

Contribution

It introduces a comparison theorem for inverse local times of reflected diffusions and demonstrates applications to Green function estimates.

Findings

Established a comparison principle for inverse local times.

Applied the comparison principle to Green function estimates.

Provided new insights into non-local operator analysis.

Abstract

In this paper, we study inverse local time at 0 of one-dimensional reflected diffusions on $[0, \infty)$, and establish a comparison principle for inverse local times. Applications to Green function estimates for non-local operators are given.