20 August, 2015
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. In this talk, I start by recalling the results that first appeared in (Haji-Ali, 2012) where I developed different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and number of particles and proposed using particle antithetic estimators for MLMC. In that work, I showed moderate savings of MLMC compared to Monte Carlo. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.