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Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing
14 references·1 citing·27 second hop
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2012Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion451 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
  • 2010Time-dependent generalized polynomial chaos173 cited
  • 2006Long-term behavior of polynomial chaos in stochastic flow simulations173 cited
  • 2013Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities70 cited
  • 2013Reduced chaos expansions with random coefficientsin reduced‐dimensional stochastic modeling of coupled problems45 cited
  • 2012Measure transformation and efficient quadrature in reduced‐dimensional stochastic modeling of coupled problems

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  • 2017A dynamical polynomial chaos approach for long-time evolution of SPDEs16 cited