Special: Lee Ricketson
Multilevel Monte Carlo for McKean-Vlasov processes, with applications to kinetic equations
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Date and time:
Tuesday, November 10, 2015 - 1:30pm
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ECCR 257
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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.