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

Abstract

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Hölder 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 BH with covariance operator Q, provided that H ∈ (1/2, 1) and tr(Q) is sufficiently small.