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Koopman Operator Spectrum for Random Dynamical System. (arXiv:1711.03146v1 [math.DS])
来源于:arXiv
In this paper we propose a generalized Koopman operator framework for
discrete and continuous time random dynamical systems. For the particular
classes of random dynamical systems, we provide the results that characterize
the spectrum and the eigenfunctions of the stochastic Koopman operator. We
discuss the relationship between the spectral properties of the generator of
the evolution and the Koopman operator family. The numerical approximations of
the spectral objects (eigenvalues, eigenfunctions) of the stochastic Koopman
operator are computed by using the state of the art DMD RRR algorithm. We
explore its behavior in the stochastic case on several test examples. Moreover,
the DMD RRR algorithm is applied in combination with the Hankel matrix and a
convergence theorem for Hankel DMD RRR in the stochastic case is proved. 查看全文>>