Seminar in Numerical Analysis: Abdul-Lateef Haji-Ali (King Abdullah University)

Monte Carlo Methods and Mean Field Approximation for Stochastic Particle Systems

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 2012, my Master thesis 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 thesis, I showed moderate savings of MLMC compared to Monte Carlo. In this talk, I recall and expand on these results, emphasizing the importance of antithetic estimators in stochastic particle systems. I will finally conclude by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.

Veranstaltung übernehmen als iCal