Abstract
In this talk, I explore the application of single level and multilevel Monte Carlo methods for computing key quantities in a stochastic particle system within the mean-field framework. The system involves stochastic particles governed by a coupled system of Ito stochastic differential equations, ultimately converging to a stochastic mean-field limit as particle numbers approach infinity. Building on prior work (Haji-Ali, 2012), I delve into various versions of Multilevel Monte Carlo (MLMC), considering both time steps and particle counts, and introduce particle antithetic estimators for MLMC. While demonstrating moderate savings compared to Monte Carlo in the earlier work, I extend these findings by proposing the utilization of our recent Multi-index Monte Carlo method to achieve enhanced convergence rates.
Brief Biography
Coming from a Computer Science background, Abdul Lateef Haji Ali obtained his Master's degree in Applied Mathematics in 2012. His master thesis was "Pedestrian Flow in the Mean-field Limit" which looked at the crowd model suggested by Helbing (1995) and studied its limit as the number of pedestrians increase. Subsequently, he pursued a Ph.D. degree in Applied Mathematics with Dr. Raul Tempone as his advisor. He is mostly interested in stochastic differential equations (SDEs) as they model particle systems.
