A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

DOI10.1142/S021902571650020XzbMath1350.60067arXiv1601.01503OpenAlexW2962859165MaRDI QIDQ2828069

Francisco J. Delgado-Vences, Franco Flandoli

Publication date: 24 October 2016

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01503

zbMATH Keywords

Hilbert spacesnumerical solutionspectral methodsstochastic PDEsFokker-Planck-Kolmogorov equations

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Fokker-Planck equations (35Q84)

Cites Work

• Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions
• Kolmogorov equations for stochastic PDEs.
• The Kolmogorov equation for a 2D-Navier-Stokes stochastic flow in a channel
• A least-squares approximation of partial differential equations with high-dimensional random inputs
• Fokker-Planck equations for SPDE with non-trace-class noise
• Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Stochastic Equations in Infinite Dimensions
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