Integration by parts formula for exit times of one dimensional diffusions

Noufel Frikha, Arturo Kohatsu-Higa, Libo Li

Published 2023-10-11Version 1

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.