Abstract
I consider the problem of integrating a function f over the d-dimensional unit cube. I describe a multilevel Monte Carlo method that estimates the integral with variance at most ϵ2 in O(d+log(d)dtϵ−2) time, for ϵ>0, where dt is the truncation dimension of f. The standard Monte Carlo method typically achieves such variance in O(dϵ−2) time. A lower bound of order d+dtϵ−2 is described for a class of multilevel Monte Carlo methods.
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