Invariant manifolds and stability for rough differential equations

2023/11/03 by Mazyar Ghani Varzaneh, Sebastian Riedel, Varzaneh, Mazyar Ghani +1
Economics, Econometrics and Finance · Engineering · Environmental Science · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Hydrology and Drought Analysis

paper · pdf · doi:10.48550/arxiv.2311.02030

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 H > (1)/(4). In case the top Lyapunov exponent is negative, we derive almost sure exponential stability of the solution.

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