Optimal Approximation of the Second Iterated Integral of Brownian Motion

DOI10.1080/07362990701540592zbMath1127.65004OpenAlexW1981593978MaRDI QIDQ5421610

A. S. Dickinson

Publication date: 24 October 2007

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990701540592

zbMATH Keywords

strong convergenceWiener processBrownian motionstochastic differential equationsKarhunen-Loéve expansionEuler-Maruyama methodWiener chaos decompositionItô diffusionGaussian Hilbert spacesecond iterated integral

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Brownian motion (60J65) Stochastic integrals (60H05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Complexity and performance of numerical algorithms (65Y20)

Related Items (5)

Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function ⋮ An Optimal Polynomial Approximation of Brownian Motion ⋮ High Order Splitting Methods for SDEs Satisfying a Commutativity Condition ⋮ An analysis of approximation algorithms for iterated stochastic integrals and a Julia and \textsc{Matlab} simulation toolbox ⋮ Asymptotically optimal approximation of some stochastic integrals and its applications to the strong second-order methods

Cites Work

• Continuous Markov processes and stochastic equations
• The Homogeneous Chaos
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