An Analysis of the Milstein Scheme for SPDEs Without a Commutative Noise Condition

DOI10.1007/978-3-030-43465-6_25OpenAlexW3094587094MaRDI QIDQ5117947

Claudine Leonhard, Andreas Rößler

Publication date: 26 August 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.03543

zbMATH Keywords

Euler schemeMilstein schemeSPDEnon-commutative noiseiterated stochastic integral

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items (3)

On the approximation and simulation of iterated stochastic integrals and the corresponding Lévy areas in terms of a multidimensional Brownian motion ⋮ A derivative-free Milstein type approximation method for SPDEs covering the non-commutative noise case ⋮ An analysis of approximation algorithms for iterated stochastic integrals and a Julia and \textsc{Matlab} simulation toolbox

Cites Work

• Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
• Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
• Iterated stochastic integrals in infinite dimensions: approximation and error estimates
• A Milstein scheme for SPDEs
• A concise course on stochastic partial differential equations
• The approximation of multiple stochastic integrals
• Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs
• Dynamics of evolutionary equations

This page was built for publication: An Analysis of the Milstein Scheme for SPDEs Without a Commutative Noise Condition