Evolution systems of measures for stochastic flows

2010/11/07 by Xiaopeng Chen, Chen, Xiaopeng, Jinqiao Duan +3
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #37H99 #60G57 #76D05 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.DS #msc:37H99 #msc:60G57 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1011.1689

14 pages

arxiv created 2010/11/07 · openalex publication_date 2010/11/07 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Random dynamical systems

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