English

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

R2 v1 2026-06-28T10:56:29.804Z