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math.DS2025
A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…
math.DS2024
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda +1
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what…