Integration by parts formula for exit times of one dimensional diffusions

TL;DR

This paper develops an integration by parts formula for the first exit time of one-dimensional diffusions, using calculus on time variables rather than traditional space-based methods, advancing probabilistic analysis techniques.

Contribution

It introduces a novel integration by parts formula for exit times of diffusions, diverging from traditional space calculus by focusing on time variable calculus methods.

Findings

Established a new integration by parts formula for exit times

Diverged from conventional methods by focusing on time variables

Enhanced probabilistic representations for diffusion processes

Abstract

In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an integration by parts formula for the first exit time of one-dimensional diffusion processes. However, our approach diverges from the conventional differential calculus applied to the associated space Markov chain; instead, we employ calculus techniques that focus on the underlying time variables.