Asymptotic stability of controlled differential equations. Part II: rough integrals
We continue the approach in Part I \cite{duchong19} to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part II deals with driving paths of finite $\nu$ - H\"older norms with $\nu \in (\fra...
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Zusammenfassung: | We continue the approach in Part I \cite{duchong19} to study stationary
states of controlled differential equations driven by rough paths, using the
framework of random dynamical systems and random attractors. Part II deals with
driving paths of finite $\nu$ - H\"older norms with $\nu \in
(\frac{1}{3},\frac{1}{2})$ so that the integrals are interpreted in the
Gubinelli sense for controlled rough paths. We prove sufficient conditions for
the attractor to be a singleton, thus the pathwise convergence is in both
pullback and forward senses. |
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DOI: | 10.48550/arxiv.1905.08236 |