Special: Lee Ricketson

Multilevel Monte Carlo for McKean-Vlasov processes, with applications to kinetic equations  

Lee Ricketson

Courant Institute of Mathematical Sciences, New York University

Date and time: 

Tuesday, November 10, 2015 - 1:30pm

Location: 

ECCR 257

Abstract: 

A wide variety of phenomena - both physical and otherwise - can be conceptualized as systems of identical, interacting particles subject to some stochastic forcing.  A rather general model of such a system is the McKean-Vlasov process: a generalization of stochastic differential equations (SDEs) that incorporates interactions between distinct “particles”.  We will discuss the extension of the multilevel Monte Carlo (MLMC) method - a popular and fast numerical method for SDEs - to McKean-Vlasov processes.  The primary challenge will be the loss of independence resulting in passage from SDEs to McKean-Vlasov processes.  As an application, we will show how kinetic equations describing plasmas and rarefied gases can be formulated in terms of McKean-Vlasov processes.  Applying our extended MLMC gives rise to a multilevel particle-in-cell method for plasmas, which we apply to the study of cyclotron beams.