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Abstract: A new concept of {\em an evolution system of measures for stochastic flows}is considered. It corresponds to the notion of an invariant measure for randomdynamical systems or cocycles. The existence of evolution systems of measuresfor asymptotically compact stochastic flows is obtained. For a white noisestochastic flow, there exists a one to one correspondence between evolutionsystems of measures for a stochastic flow \emph{and} evolution systems ofmeasures for the associated Markov transition semigroup. As an application, analternative approach for evolution systems of measures of 2D stochasticNavier-Stokes equations with a time-periodic forcing term is presented.



Author: Xiaopeng Chen, Jinqiao Duan, Michael Scheutzow

Source: https://arxiv.org/







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