Asymptotical stability of differential equations driven by Hölder--continuous paths

2016/04/21 by María J. Garrido–Atienza, María J. Garrido-Atienza, Garrido-Atienza, María J. +4
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #math.DS

paper · pdf · doi:10.48550/arxiv.1604.06213

18 pages

arxiv created 2016/04/21 · openalex publication_date 2016/04/21 · arxiv updated 2016/04/22 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by Hölder--continuous paths with Hölder 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.

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