---
res:
  bibo_abstract:
  - "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.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Friedrich
      foaf_name: Philipp, Friedrich
      foaf_surname: Philipp
  - foaf_Person:
      foaf_givenName: Manuel
      foaf_name: Schaller, Manuel
      foaf_surname: Schaller
  - foaf_Person:
      foaf_givenName: Karl
      foaf_name: Worthmann, Karl
      foaf_surname: Worthmann
  - foaf_Person:
      foaf_givenName: Sebastian
      foaf_name: Peitz, Sebastian
      foaf_surname: Peitz
      foaf_workInfoHomepage: http://www.librecat.org/personId=47427
    orcid: 0000-0002-3389-793X
  - foaf_Person:
      foaf_givenName: Feliks
      foaf_name: Nüske, Feliks
      foaf_surname: Nüske
  bibo_doi: 10.1016/j.acha.2024.101657
  bibo_volume: 71
  dct_date: 2024^xs_gYear
  dct_language: eng
  dct_publisher: Springer @
  dct_title: Error bounds for kernel-based approximations of the Koopman operator@
...