Monte Carlo convergence rates for kth moments in Banach spaces

We formulate standard and multilevel Monte Carlo methods for the kth moment M_ε^k[ξ] of a Banach space valued random variable ξ:Ω→E, interpreted as an element of the k-fold injective tensor product space ⊗_ε^kE. For the standard Monte Carlo estimator of M_ε^k[ξ], we prove the k...