Lower path regularity in all dimensions

Michael Hinz; Jonas M. Tölle; Lauri Viitasaari

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arXiv · 2605.27713

Lower path regularity in all dimensions

Michael Hinz·Jonas M. Tölle·Lauri Viitasaari

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Abstract

We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions $d\geq 1$. Examples include Gaussian processes, in particular, fractional Brownian motions with Hurst index $H\in (0,1)$, Rosenblatt processes, and solutions to stochastic differential equations driven by fractional Brownian motions with Hurst index $H\in (\frac{1}{4},1)$, all in arbitrary dimensions $d\ge 1$. Our key tool is a new continuity result for Riesz potentials of occupation measures, which we use as substitutes for local times.

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Michael Hinz, Jonas M. Tölle, Lauri Viitasaari. 2026-05-26. Lower path regularity in all dimensions. https://arxiv.org/abs/2605.27713

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