Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

Journal article (2020)

Authors

Sonja Cox Universiteit van Amsterdam
Martin Hutzenthaler Universität Duisburg-Essen
Arnulf Jentzen ETH Zürich, University of Münster
J.M.A.M. van Neerven Analysis - EEMCS
Timo Welti ETH Zürich
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2020 Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, J.M.A.M. van Neerven, Timo Welti
DOI: https://doi.org/10.1093/imanum/drz063
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.

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