Regularity of Local times associated to Volterra-Lévy processes and path-wise regularization of stochastic differential equations

Fabian A. Harang; Chengcheng Ling

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arXiv · 2007.01093

Regularity of Local times associated to Volterra-Lévy processes and path-wise regularization of stochastic differential equations

Fabian A. Harang·Chengcheng Ling

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Abstract

We investigate the space-time regularity of the local time associated to Volterra-Lévy processes, including Volterra processes driven by $α$-stable processes for $α\in(0,2]$. We show that the spatial regularity of the local time for Volterra-Lévy process is $P$-a.s. inverse proportionally to the singularity of the associated Volterra kernel. We apply our results to the investigation of path-wise regularizing effects obtained by perturba\Ption of ODEs by a Volterra-Lévy process which has sufficiently regular local time. Following along the lines of [15], we show existence, uniqueness and differentiablility of the flow associated to such equations.

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BibTeX RIS

Fabian A. Harang, Chengcheng Ling. 2021-04-06. Regularity of Local times associated to Volterra-Lévy processes and path-wise regularization of stochastic differential equations. https://arxiv.org/abs/2007.01093

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