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    Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo

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    Type
    Conference Paper
    Authors
    Hoel, Hakon
    Häppölä, Juho
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-06-14
    Online Publication Date
    2016-06-14
    Print Publication Date
    2016
    Permanent link to this record
    http://hdl.handle.net/10754/622138
    
    Metadata
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    Abstract
    A formal mean square error expansion (MSE) is derived for Euler-Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise, a posteriori, adaptive time-stepping Euler-Maruyama algorithm for numerical solutions of SDE, and the resulting algorithm is incorporated into a multilevel Monte Carlo (MLMC) algorithm for weak approximations of SDE. This gives an efficient MSE adaptive MLMC algorithm for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC algorithm is shown to outperform the uniform time-stepping MLMC algorithm by orders of magnitude, producing output whose error with high probability is bounded by TOL > 0 at the near-optimal MLMC cost rate б(TOL log(TOL)) that is achieved when the cost of sample generation is б(1).
    Citation
    Hoel H, Häppölä J, Tempone R (2016) Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods: 29–86. Available: http://dx.doi.org/10.1007/978-3-319-33507-0_2.
    Publisher
    Springer Nature
    Journal
    Springer Proceedings in Mathematics & Statistics
    Conference/Event name
    11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014
    DOI
    10.1007/978-3-319-33507-0_2
    arXiv
    1411.5515
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-33507-0_2
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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