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We analyse a multilevel Monte Carlo method for the approximation ofdistribution functions of univariate random variables. Since, by assumption,the target distribution is not known explicitly, approximations have to beused. We provide an asymptotic analysis of the error and the cost of thealgorithm. Furthermore we construct an adaptive version of the algorithm thatdoes not require any a priori knowledge on weak or strong convergence rates. Weapply the adaptive algorithm to smooth path-independent and path-dependentfunctionals and to stopped exit times of SDEs.

Adaptive Multilevel Monte Carlo Approximation of Distribution Functions