Naslov
Stochastic Koopman operator and the numerical approximations of its spectral objects

Autori
Črnjarić-Žic, Nelida

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
Operator Theoretic Methods in Dynamic Data Analysis and Control, IPAM workshop / - Los Angeles (CA), 2019, 1-1

Skup
Operator Theoretic Methods in Dynamic Data Analysis and Control, IPAM workshop

Mjesto i datum
Los Angeles (CA), Sjedinjene Američke Države, 11.02.2019. - 15.02.2019

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Koopman operator, Koopman eigenvalues and eigenfunctions, spectral objects, numerical algorithms

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

POVEZANOST RADA