Year: 2019
Type: preprint
Abstract: 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 $ν$ - Hölder norms with $ν\in (\frac{1}{3},\frac{1}{2})$ 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.
Source: arXiv (Cornell University)
Author: Duc, Luu Hoang
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3041608352