A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup
Probability
2024-06-10 v2
Abstract
We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as the expected value of a functional of a reflected diffusion process. Furthermore, as an application, we obtain a Bismut-Elworthy-Li formula which is also valid at the boundary.
Keywords
Cite
@article{arxiv.2312.07084,
title = {A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup},
author = {Dan Crisan and Arturo Kohatsu-Higa},
journal= {arXiv preprint arXiv:2312.07084},
year = {2024}
}