2019/05/13 by Luu Hoang Duc, Duc, Luu Hoang, Phan Thanh Hong +1
Engineering · #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1905.04945
openalex publication_date 2019/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite p-variations with 1 ≤ p <2 so that the integrals are interpreted in the Young sense. Our method helps to generalize recent results \citeGAKLBSch2010, \citeducGANSch18, \citeduchongcong18 on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both pullback and forward senses.