# Stability theory for Gaussian rough differential equations. Part I

## TL;DR

This paper introduces a direct method to establish the exponential stability of solutions to Gaussian rough differential equations with dissipative drifts under small noise, extending stability analysis in rough path theory.

## Contribution

It provides a novel quantitative approach for proving stability of Gaussian rough differential equations, specifically under strongly dissipative conditions.

## Key findings

- Trivial solution is exponentially stable under small noise.
- The method applies to Gaussian rough differential equations with dissipative drifts.
- Provides a new stability proof technique in rough path analysis.

## Abstract

We propose a quantitative direct method of proving the stability result for Gaussian rough differential equations in the sense of Gubinelli \cite{gubinelli}. Under the strongly dissipative assumption of the drift coefficient function, we prove that the trivial solution of the system under small noise is exponentially stable.