Asymptotical Stability of Differential Equations Driven by Hölder Continuous Paths

• DOI: 10.1007/s10884-017-9574-6
• Publication Date: 2017-01-18T15:14:32Z
• Authors: María J. Garrido-...; Andreas Neuenkirch; Björn Schmalfuß
• Keywords: Hurst exponent; Fractional Brownian motion; Hölder condition

18 pages<br/>In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by H��lder--continuous paths with H��lder exponent greater than $1/2$. This applies in particular to stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than $1/2$. We motivate the study of local stability by giving a particular example of a scalar equation, where global stability of the trivial solution can be obtained.<br/>