Håkon Andreas Hoel: Overview of the Multilevel Monte Carlo method

The multilevel Monte Carlo (MLMC) method is a relatively recent method that offers a compelling approach to tackling computational challenges in approximations of quantities of interest. This talk presents the fundamentals of the method and describes its advantages over traditional Monte Carlo techniques in settings with complicated distributions, whose samples have to be approximated by numerical methods. We also present different applications of MLMC: solving stochastic differential equations, state estimation in data assimilation, solving partial differential equations with random input, and for sampling a posterior measure in high dimensional state space by multilevel Markov Chain Monte Carlo simulations.