Complexity of parametric integration in various smoothness classes

We continue the complexity analysis of parametric definite and indefinite integration given by the authors in [2]. Here we consider anisotropic classes of functions, including certain classes with dominating mixed derivatives. Our analysis is based on a multilevel Monte Carlo method developed in [2] and we obtain the order of the deterministic and randomized n-th minimal errors (in some limit cases up to logarithms). Furthermore, we compare the rates in the deterministic and randomized setting to assess the gain reached by randomization.