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arXiv · 1705.01573

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

Luu Hoang Duc·María J. Garrido-Atienza·Andreas Neuenkirch·Björn Schmalfuß
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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.

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Luu Hoang Duc, María J. Garrido-Atienza, Andreas Neuenkirch, Björn Schmalfuß. 2017-05-03. Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in $(1/2,1)$. https://arxiv.org/abs/1705.01573

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