Higher order QMC rules for uncertainty quantification using periodic random variables

A popular model for the parametrization of random fields in uncertainty quantification is given by the so-called affine model, where the input random field is assumed to depend on uniformly distributed random variables in a linear manner. In this talk, we consider a different -- yet equally valid -- model for the input random field, where the random variables enter the input field as periodic functions instead. The field can be constructed to have the same mean and covariance function as the affine random field. This setting allows us to construct simple lattice QMC rules that obtain higher order convergence rates, which we apply to elliptic PDEs equipped with random coefficients.

This is a joint work with Frances Kuo and Ian Sloan.