Pregled bibliografske jedinice broj: 956515
Koopman Operator Spectrum for Random Dynamical Systems
Koopman Operator Spectrum for Random Dynamical Systems // Journal of nonlinear science, 2019 (2019), 09582-z, 50 doi:10.1007/s00332-019-09582-z (međunarodna recenzija, članak, znanstveni)
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Naslov
Koopman Operator Spectrum for Random Dynamical Systems
Autori
Črnjarić-Žic, Nelida ; Maćešić, Senka ; Mezić, Igor
Izvornik
Journal of nonlinear science (0938-8974) 2019
(2019);
09582-z, 50
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
stochastic Koopman operator, random dynamical systems, stochastic differential equations, dynamic mode decomposition
Sažetak
In this paper we propose a generalized Koopman operator framework for discrete and continuous time random dynamical systems. For the particular classes of ran- dom 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 (eigenval- ues, 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.
Izvorni jezik
Engleski
Znanstvena područja
Matematika, Temeljne tehničke znanosti
POVEZANOST RADA
Ustanove:
Tehnički fakultet, Rijeka
