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arXiv · 2306.02803

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

Takuya Nakagawa·Ryoichi Suzuki
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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.

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Takuya Nakagawa, Ryoichi Suzuki. 2023-06-05. Existence of density functions for SDEs driven by pure-jump processes. https://doi.org/10.15559/24-vmsta245

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