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arXiv · 1605.00856

Convergence in H\"older norms with applications to Monte Carlo methods in infinite dimensions

Sonja Cox·Martin Hutzenthaler·Arnulf Jentzen·Jan van Neerven·Timo Welti
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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 which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect to much stronger H\"older norms and the convergence rate is essentially reduced by the H\"older 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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Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen, Jan van Neerven, Timo Welti. 2016-05-03. Convergence in H\"older norms with applications to Monte Carlo methods in infinite dimensions. https://doi.org/10.1093/imanum/drz063

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