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arXiv · 1011.1689

Evolution systems of measures for stochastic flows

Xiaopeng Chen·Jinqiao Duan·Michael Scheutzow
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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 random dynamical systems (or cocycles). The existence of evolution systems of measures for asymptotically compact stochastic flows is obtained. For a white noise stochastic flow, there exists a one to one correspondence between evolution systems of measures for a stochastic flow \emph{and} evolution systems of measures for the associated Markov transition semigroup. As an application, an alternative approach for evolution systems of measures of 2D stochastic Navier-Stokes equations with a time-periodic forcing term is presented.

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Xiaopeng Chen, Jinqiao Duan, Michael Scheutzow. 2010-11-07. Evolution systems of measures for stochastic flows. https://arxiv.org/abs/1011.1689

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