Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise

DOI10.1137/16M1094087zbMath1432.65161arXiv1509.08427OpenAlexW2886623333MaRDI QIDQ4581904

Claudine Leonhard, Andreas Rößler

Publication date: 21 August 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.08427

zbMATH Keywords

stochastic differential equationnumerical approximationstochastic partial differential equationMilstein schemeSPDEstochastic evolution equation\(Q\)-Wiener processhigher-order approximationSDEcommutative noisederivative-free approximation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (5)

A derivative-free Milstein type approximation method for SPDEs covering the non-commutative noise case ⋮ An Analysis of the Milstein Scheme for SPDEs Without a Commutative Noise Condition ⋮ An analysis of approximation algorithms for iterated stochastic integrals and a Julia and \textsc{Matlab} simulation toolbox ⋮ Iterated stochastic integrals in infinite dimensions: approximation and error estimates ⋮ A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations

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