Invariant manifolds and stability for rough differential equations
Probability
2025-07-15 v3 Dynamical Systems
Abstract
We prove the existence of local stable, unstable, and center manifolds for stochastic semiflows induced by rough differential equations driven by rough paths valued stochastic processes around random fixed points of the equation. Examples include stochastic differential equations driven by a fractional Brownian motion with Hurst parameter . In case the top Lyapunov exponent is negative, we derive almost sure exponential stability of the solution.
Cite
@article{arxiv.2311.02030,
title = {Invariant manifolds and stability for rough differential equations},
author = {Mazyar Ghani Varzaneh and Sebastian Riedel},
journal= {arXiv preprint arXiv:2311.02030},
year = {2025}
}