Location: ICIAM2015, Beijing, China
Title: Optimization of mesh hierarchies in Multilevel Monte Carlo samplers
Abstract:
We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and non-geometric sequences of mesh sizes and show that geometric hierarchies are nearly optimal and have the same asymptotic computational complexity as non-geometric optimal hierarchies. To provide numerical grounds for our theoretical results, we test our hierarchies with the Continuation MLMC Algorithm.
Title: Monte Carlo Methods for Particle System
Abstract:
We discuss using Monte Carlo methods to compute quantities of interests of a stochastic particle system, where each particle follows a stochastic differential equation. The particle system is assumed to converge to some mean-field limit as the number of particles tend to infinity. In that setting, we discuss how to apply Multilevel Monte Carlo and Multi-index Monte Carlo and the computational advantages of using these methods.