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    PC analysis of stochastic differential equations driven by Wiener noise

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    Type
    Article
    Authors
    Le Maitre, Olivier
    Knio, Omar
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Clean Combustion Research Center
    Date
    2015-03
    Permanent link to this record
    http://hdl.handle.net/10754/564078
    
    Metadata
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    Abstract
    A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.
    Sponsors
    This work was supported by the US Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC0008789.
    Publisher
    Elsevier BV
    Journal
    Reliability Engineering & System Safety
    DOI
    10.1016/j.ress.2014.11.002
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.ress.2014.11.002
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Clean Combustion Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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