We investigate the space-time regularity of the local time associated with Volterra–Lévy processes, including Volterra processes driven by \(\alpha \)-stable processes for \(\alpha \in (0,2]\). We show that the spatial regularity of the local time for Volterra–Lévy process is \({\mathbb {P}}\)-a.s. inverse proportional to the singularity of the associated Volterra kernel. We apply our results to the investigation of path-wise regularizing effects obtained by perturbation of ordinary differential equations by a Volterra–Lévy process which has sufficiently regular local time. Following along the lines of Harang and Perkowski (2020), we show existence, uniqueness and differentiability of the flow associated with such equations.

我们研究了与 Volterra–Lévy 过程相关的本地时间的时空规律，包括由\(\alpha \)驱动的 Volterra过程 - 对于\(\alpha \in (0,2]\) 的稳定过程。我们表明Volterra–Lévy 过程本地时间的空间规律是\({\mathbb {P}}\) - 与相关的 Volterra 核的奇异性成反比。我们将我们的结果应用于路径正则化效应的研究通过具有足够规则本地时间的 Volterra-Lévy 过程对常微分方程进行微扰获得。按照 Harang 和 Perkowski (2020) 的思路，我们展示了与此类方程相关的流动的存在性、唯一性和可微性。