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

By Luu Hoang Duc, María J. Garrido-Atienza, Andreas Neuenkirch, B. Schmalfuβ. 2017

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This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Holder continuous functions with Holder 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.

Subfields: Control and Systems Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4046e2b172b4127f3d92fa7935b7781b149eeae1