MS25 - Advanced multilevel Monte Carlo methods 

Håkon Hoel, Kody Law, Raul Tempone 

Abstract 

For weak approximations of stochastic problems that require numerical pproximation, the computational cost to obtain a given level of accuracy by a plain vanilla Monte Carlo approach can be very high. The multilevel Monte Carlo approach consists of introducing a telescopic sum of different resolution, coupled numerical approximations with decreasing variance, such that the number of necessary samples is progressively reduced for the more expensive fine resolution samples. This can considerably reduce the total cost of obtaining a given accuracy. There has been a lot of research activity recently in extending the plain vanilla Monte Carlo to more advanced multilevel Monte Carlo methods involving higher dimensional PDEs and inference in static and sequential contexts. This minisymposium aims to bring together experts in the field to share their most recent advances.