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| \title{\textbf{Random Dynamical Systems in Banach Spaces}}
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We consider linear and nonlinear nonautonomous random evolution equations given by
$$u'(t)=A(\theta_{t})u+F(\theta_{t},u),\hspace*{2 mm} u(0):=x\in X,$$
where $X$ is a separable Banach space and $(\theta_{t})_{t\in\mathbb{R}}$ is a metric dynamical system.
We give conditions under which such equations generate random dynamical systems
and present important applications.
Finally, the long-time behaviour of
the corresponding random dynamical systems is studied by means of a multiplicative ergodic theorem proved in \cite{lian}.
Stable and unstable manifolds are also discussed.
\begin{thebibliography}{99}
\bibitem{amann} H. Amann, \textit{Linear and Quasilinear Parabolic Problems}. Basel; Boston; Berlin: Birkh\"auser, Vol. 1, 1995
\bibitem{lian} Z. Lian, K. Lu, \textit{Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space}. Mem. Amer. Math. Soc., Vol. 206, Nr. 967, 2010
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