Print Email Facebook Twitter Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions Title Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions Author Cox, Sonja (Universiteit van Amsterdam) Hutzenthaler, Martin (Universität Duisburg-Essen) Jentzen, Arnulf (University of Münster; ETH Zürich) van Neerven, J.M.A.M. (TU Delft Analysis) Welti, Timo (ETH Zürich) Date 2020 Abstract We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process that is strongly Hölder continuous in time, then this sequence converges in the strong sense even with respect to much stronger Hölder norms and the convergence rate is essentially reduced by the Hölder exponent. Our first application hereof establishes pathwise convergence rates for spectral Galerkin approximations of stochastic partial differential equations. Our second application derives strong convergence rates of multilevel Monte Carlo approximations of expectations of Banach-space-valued stochastic processes. To reference this document use: http://resolver.tudelft.nl/uuid:19f381e9-2326-4394-b79a-eda34013d6e0 DOI https://doi.org/10.1093/imanum/drz063 Embargo date 2020-10-28 ISSN 1464-3642 Source IMA Journal of Numerical Analysis, 41 (2021) (1), 493–548 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2020 Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, J.M.A.M. van Neerven, Timo Welti Files PDF IMA_2021.pdf 738.7 KB Close viewer /islandora/object/uuid:19f381e9-2326-4394-b79a-eda34013d6e0/datastream/OBJ/view