Local Stability of Differential Equations Driven by Hölder-Continuous Paths with Hölder Index in (1/3,1/2)
María José Garrido-Atienza, Björn Schmalfuß · SIAM Journal on Applied Dynamical Systems · 2018
We study the longtime behavior of solutions to differential equations perturbed with very general Hölder-continuous functions with Hölder index between 1/3 and 1/2. To be more precise, we establish local exponential stability for the solutions of these equations, where localness means that the initial condition belongs to a random neighborhood of zero.