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In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS).
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B.O. Koopman · 1931
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Dynamic mode decomposition of numerical and experimental data
P.J. Schmid · 2008
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Spectral analysis of nonlinear flows
C.W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D.S. Henningson · 2009
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Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations
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P.J. Schmid, L. Li, M.P. Juniper, and O. Pust · 2011
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M. Budišić, R. Mohr, and I. Mezić · 2012
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M.O. Williams, I.G. Kevrekidis, and C.W. Rowley · 2015
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Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
G. Fantuzzi, D. Goluskin, D. Huang, and S.I. Chernyshenko · 2016
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On the numerical approximation of the Perron-Frobenius and Koopman operator
S. Klus, P. Koltai, and C. Schütte · 2016
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Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator
S. Klus and C. Schütte · 2016
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Koopman mode decomposition for periodic/quasi-periodic time dependence
I. Mezić and A. Surana · 2016
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