{"_id":"38031","department":[{"_id":"655"}],"external_id":{"arxiv":["2301.08637"]},"type":"preprint","citation":{"short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, ArXiv:2301.08637 (2023).","mla":"Philipp, Friedrich, et al. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>ArXiv:2301.08637</i>, 2023.","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds for kernel-based approximations of the Koopman operator,” <i>arXiv:2301.08637</i>. 2023.","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2023, title={Error bounds for kernel-based approximations of the Koopman operator}, journal={arXiv:2301.08637}, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2023} }","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2023). Error bounds for kernel-based approximations of the Koopman operator. In <i>arXiv:2301.08637</i>.","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>ArXiv:2301.08637</i>, 2023.","ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based approximations of the Koopman operator. <i>arXiv:230108637</i>. Published online 2023."},"publication":"arXiv:2301.08637","title":"Error bounds for kernel-based approximations of the Koopman operator","author":[{"last_name":"Philipp","first_name":"Friedrich","full_name":"Philipp, Friedrich"},{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"last_name":"Worthmann","first_name":"Karl","full_name":"Worthmann, Karl"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Nüske","first_name":"Feliks","full_name":"Nüske, Feliks"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2301.08637"}],"language":[{"iso":"eng"}],"user_id":"47427","status":"public","date_created":"2023-01-23T07:03:39Z","abstract":[{"text":"We consider the data-driven approximation of the Koopman operator for\r\nstochastic differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus is on the estimation error if the data are collected from long-term\r\nergodic simulations. We derive both an exact expression for the variance of the\r\nkernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic bounds for the finite-data estimation error. Moreover, we derive\r\na bound on the prediction error of observables in the RKHS using a finite\r\nMercer series expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck process illustrate our results.","lang":"eng"}],"oa":"1","year":"2023","date_updated":"2023-01-23T07:04:12Z"}