Multi-level Monte Carlo algorithms for infinite-dimensional integration on RNRN

We study randomized algorithms for numerical integration with respect to a product probability measure on the sequence space RNRN. We consider integrands from reproducing kernel Hilbert spaces, whose kernels are superpositions of weighted tensor products. We combine tractability results for finite-dimensional integration with the multi-level technique to construct new algorithms for infinite-dimensional integration. These algorithms use variable subspace sampling, and we compare the power of variable and fixed subspace sampling by an analysis of minimal errors.