# Stability theory for Gaussian rough differential equations. Part II

## TL;DR

This paper develops a quantitative method to establish exponential stability of solutions to Gaussian rough differential equations with dissipative drift, extending stability analysis in the rough paths framework.

## Contribution

It introduces a direct, quantitative approach to prove stability for Gaussian rough differential equations under dissipative conditions, advancing the theoretical understanding.

## Key findings

- Trivial solution is exponentially stable under small noise.
- Provides a new method for stability analysis in rough differential equations.
- Extends stability results to Gaussian noise settings.

## 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.