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

@article{Cox2016ConvergenceIH, title={Convergence in H\"older norms with applications to Monte Carlo methods in infinite dimensions}, author={Sonja Cox and Martin Hutzenthaler and Arnulf Jentzen and Jan van Neerven and Timo Welti}, journal={arXiv: Numerical Analysis}, year={2016} }

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… CONTINUE READING

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