On Stratonovich and Skorohod stochastic calculus for Gaussian processes

TL;DR

This paper develops change of variables formulas for multidimensional Gaussian processes with very low regularity, using a combination of rough paths theory and stochastic analysis to extend stochastic calculus tools.

Contribution

It introduces Stratonovich and Skorohod formulas for Gaussian processes with H"older regularity below 1/4, bridging rough paths and stochastic calculus methods.

Findings

Derived change of variables formulas for irregular Gaussian processes.

Extended stochastic calculus to processes with low regularity.

Combined rough paths and stochastic analysis techniques.

Abstract

In this article, we derive a Stratonovich and Skorohod type change of variables formula for a multidimensional Gaussian process with low H\"older regularity (typically lower than 1/4). To this aim, we combine tools from rough paths theory and stochastic analysis.