Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing

DOI10.1137/15M1019167zbMath1346.60108arXiv1505.00047MaRDI QIDQ5741194

Guillaume Bal, Hasan Çağan Özen

Publication date: 22 July 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.00047

zbMATH Keywords

stochastic differential equationsMarkov processesuncertainty quantificationpolynomial chaos expansions

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Random operators and equations (aspects of stochastic analysis) (60H25) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Uses Software

• OPQ

Cites Work

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• Polynomial diffusions and applications in finance
• Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities
• Uncertainty propagation using Wiener-Haar expansions
• Time-dependent generalized polynomial chaos
• Long-term behavior of polynomial chaos in stochastic flow simulations
• Test models for improving filtering with model errors through stochastic parameter estimation
• Density questions in the classical theory of moments
• Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
• A class of orthogonal polynomials
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• On the convergence of generalized polynomial chaos expansions
• Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
• Reduced chaos expansions with random coefficientsin reduced-dimensional stochastic modeling of coupled problems
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Spectral Methods for Uncertainty Quantification
• On the relation between the multidimensional moment problem and the one-dimensional moment problem.
• A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations
• Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
• Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
• Stochastic Navier--Stokes Equations for Turbulent Flows
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• A HYBRID GENERALIZED POLYNOMIAL CHAOS METHOD FOR STOCHASTIC DYNAMICAL SYSTEMS
• High-Order Collocation Methods for Differential Equations with Random Inputs
• Stochastic differential equations. An introduction with applications.