Existence of density functions for SDEs driven by pure-jump processes
Probability
2025-10-30 v2
Abstract
We verify the existence of density functions of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a non-truncated stable process. This is proved by the existence of density functions of the running maximum of Wiener-Poisson functionals resulting from Bismut's approach to Malliavin calculus for jump processes.
Keywords
Cite
@article{arxiv.2306.02803,
title = {Existence of density functions for SDEs driven by pure-jump processes},
author = {Takuya Nakagawa and Ryoichi Suzuki},
journal= {arXiv preprint arXiv:2306.02803},
year = {2025}
}
Comments
21 pages