paper

Existence of density functions for SDEs driven by pure-jump processes

arXiv:2306.02803 · doi:10.15559/24-VMSTA245

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.

21 pages

Existence of density functions for SDEs driven by pure-jump processes · wovepaper