A multiparameter Stochastic Sewing lemma and the regularity of local times associated to Gaussian sheets

TL;DR

This paper extends the stochastic sewing lemma to multiple parameters, enabling new regularity estimates for local times of Gaussian fields and revealing how noise regularizes SDEs, with boundary effects playing a key role.

Contribution

It introduces a multiparameter stochastic sewing lemma and applies it to derive novel regularity results for Gaussian field local times and SDE regularization.

Findings

Regularity estimates for local times of Gaussian sheets.

Regularization by noise effects in SDEs due to boundary terms.

Additive contribution of each parameter to regularization effects.

Abstract

We establish a multiparameter extension of the stochastic sewing lemma. This allows us to derive novel regularity estimates on the local time of locally non-deterministic Gaussian fields. These estimates are sufficiently strong to derive regularization by noise results for SDEs in the plain. In this context, we make the interesting and rather surprising observation that regularization effects profiting from each parameter of the underlying stochastic field in an additive fashion usually appear to be due to boundary terms of the driving stochastic field.