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dc.contributor.authorLe Maitre, Olivier
dc.contributor.authorKnio, Omar
dc.date.accessioned2015-08-03T12:31:09Z
dc.date.available2015-08-03T12:31:09Z
dc.date.issued2015-03
dc.identifier.citationLe Maître, O. P., & Knio, O. M. (2015). PC analysis of stochastic differential equations driven by Wiener noise. Reliability Engineering & System Safety, 135, 107–124. doi:10.1016/j.ress.2014.11.002
dc.identifier.issn09518320
dc.identifier.doi10.1016/j.ress.2014.11.002
dc.identifier.urihttp://hdl.handle.net/10754/564078
dc.description.abstractA 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.
dc.description.sponsorshipThis work was supported by the US Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC0008789.
dc.publisherElsevier BV
dc.subjectPolynomial chaos
dc.subjectStochastic differential equation
dc.subjectVariance analysis
dc.subjectWiener noise
dc.titlePC analysis of stochastic differential equations driven by Wiener noise
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentClean Combustion Research Center
dc.identifier.journalReliability Engineering & System Safety
dc.contributor.institutionLIMSI-CNRS, rue John von NeumannOrsay Cedex, France
dc.contributor.institutionDepartment of Mechanical Engineering and Materials Science, Duke UniversityDurham, NC, United States
kaust.personKnio, Omar
kaust.personLe Maitre, Olivier


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