Mathematics > Probability
[Submitted on 5 Jun 2023
(v1)
, last revised 29 Oct 2025 (this version, v2)]
Title: Existence of density functions for SDEs driven by pure-jump processes
Title: 纯跳跃过程驱动的SDE的概率密度函数的存在性
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.
Submission history
From: Takuya Nakagawa [view email][v1] Mon, 5 Jun 2023 11:57:08 UTC (15 KB)
[v2] Wed, 29 Oct 2025 04:12:21 UTC (15 KB)
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