# Asymptotic stability for stochastic dissipative systems with a H\"older noise

## TL;DR

This paper proves exponential stability and existence of a random attractor for stochastic dissipative systems driven by H"older noise, extending stability analysis to systems influenced by fractional Brownian motion.

## Contribution

It introduces new stability results for stochastic systems with H"older noise, including fractional Brownian motion, under strong dissipativity assumptions.

## Key findings

- Exponential stability of the zero solution established.
- Existence of a random pullback attractor demonstrated.
- Results apply to systems with multiplicative fractional Brownian noise.

## Abstract

We prove the exponential stability of the zero solution of a stochastic differential equation with a H\"older noise, under the strong dissipativity assumption. As a result, we also prove that there exists a random pullback attractor for a stochastic system under a multiplicative fractional Brownian noise.