Multilevel Monte Carlo Approximation of Distribution Functions and Densities

Michael B. Giles, Tigran Nagapetyan, Klaus Ritter
2015 SIAM/ASA Journal on Uncertainty Quantification  
We construct and analyze multi-level Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable assumptions on the weak and strong convergence. We apply the results to smooth path-independent and path-dependent functionals and to stopped exit times of SDEs. Mathematical Institute,
doi:10.1137/140960086 fatcat:eakffdp5avblpn4ndjwt7jmxeq