Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions
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Date
2021-01Type
- Journal Article
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. Show more
Publication status
publishedExternal links
Journal / series
IMA Journal of Numerical AnalysisVolume
Pages / Article No.
Publisher
Oxford University PressOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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