PC analysis of stochastic differential equations driven by Wiener noise

Olivier Le Maitre, Omar Knio

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)107-124
Number of pages18
JournalReliability Engineering & System Safety
Volume135
DOIs
StatePublished - Mar 2015

ASJC Scopus subject areas

  • Applied Mathematics
  • Industrial and Manufacturing Engineering
  • Safety, Risk, Reliability and Quality

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