# Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in $(1/2,1)$

## TL;DR

This paper investigates the exponential stability of certain stochastic evolution equations driven by fractional Brownian motion with Hurst parameter in (1/2,1), establishing stability conditions based on the properties of the noise.

## Contribution

It provides new stability results for evolution equations influenced by fractional Brownian motion with Hurst parameter greater than 1/2, extending existing theory to this class of stochastic systems.

## Key findings

- Exponential stability is achieved under small covariance operator trace.
- Results apply to equations driven by fractional Brownian motion with Hurst parameter in (1/2,1).
- Stability conditions depend on the H"older continuity and noise characteristics.

## Abstract

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations whose noisy inputs are given by a fractional Brownian motion $B^H$ with covariance operator $Q$, provided that $H\in (1/2,1)$ and ${\rm tr}(Q)$ is sufficiently small.