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    A study of Monte Carlo methods for weak approximations of stochastic particle systems in the mean-field?

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    Type
    Presentation
    Authors
    Haji Ali, Abdul Lateef cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-01-08
    Permanent link to this record
    http://hdl.handle.net/10754/624865
    
    Metadata
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    Abstract
    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. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
    Collections
    Applied Mathematics and Computational Science Program; Presentations; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

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