Stochastic Koopman operator and the numerical approximations of its spectral objects (CROSBI ID 680925)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Črnjarić-Žic, Nelida
engleski
Stochastic Koopman operator and the numerical approximations of its spectral objects
A generalization of the Koopman operator framework, originally developed for deterministic dynamical systems, to discrete and continuous time random dynamical systems (RDS) results with the stochastic Koopman operators. We provide the results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator associated with different types of linear RDS. Then we consider the RDS for which the associated Koopman operator family is a semigroup, especially those for which the generator can be determined. We propose different approaches for using the data-driven DMD algorithms in the stochastic framework to approximate numerically the spectral objects (eigenvalues, eigenfunctions) of the stochastic Koopman operator. We prove that, under certain assumptions, the outputs of the stochastic Hankel DMD (sHankel-DMD) algorithm converge to the true stochastic Koopman eigenvalues and eigenfunctions. We apply the methodology to a variety of examples, revealing objects in spectral expansions of the stochastic Koopman operator.
Koopman operator, Koopman eigenvalues and eigenfunctions, spectral objects, numerical algorithms
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Podaci o prilogu
1-1.
2019.
objavljeno
Podaci o matičnoj publikaciji
Operator Theoretic Methods in Dynamic Data Analysis and Control, IPAM workshop
Los Angeles (CA):
Podaci o skupu
Operator Theoretic Methods in Dynamic Data Analysis and Control, IPAM workshop
pozvano predavanje
11.02.2019-15.02.2019
Los Angeles (CA), Sjedinjene Američke Države