On the global error of Itô--Taylor schemes for strong approximation of scalar stochastic differential equations
type: Item
instance of: scholarly article
title: On the global error of Itô--Taylor schemes for strong approximation of scalar stochastic differential equations
zbMATH Open document ID: 1068.65013
author: Norbert Hofmann
author: Thomas Müller-Gronbach
published in: Journal of Complexity
publication date: 2004-11-23T00:00:00Z
review text: From the viewpoint of computational cost, the authors study the error incurred by Itô-Taylor methods for approximating the solution of the Itô stochastic differential equation \[ dX(t)= a(t, X(t))\,dt+ b(t, X(t))\,dW(t),\quad 0\leq t\leq 1. \] Two theorems on this are proved. The main result obtained is that the order of error with respect to \(N\), the number of multiple Itô integrals evaluated in applying the numerical method, is at best of order \(N^{-{1\over 2}}\).
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 2117870
zbMATH Keywords: pathwise approximation
zbMATH Keywords: Itô-Taylor methods
zbMATH Keywords: optimal order of convergence
zbMATH Keywords: Itô stochastic differential equation
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
full work available at URL: j.jco.2003.09.004
OpenAlex ID: W2003895317
cites work: The optimal discretization of stochastic differential equations
cites work: Linear vs standard information for scalar stochastic differential equations
cites work: Q4714065
cites work: Q4319807
cites work: The optimal uniform approximation of systems of stochastic differential equations
cites work: Q3048009
DOI: 10.1016/J.JCO.2003.09.004
Recommended article: Strongly asymptotically optimal schemes for the strong approximation of stochastic differential equations with respect to the supremum error
Recommended article: Strong approximation for Itô stochastic differential equations
Recommended article: An estimate of the error for strong solutions of stochastic differential equations
Recommended article: Minimal Errors for Strong and Weak Approximation of Stochastic Differential Equations
Recommended article: A family of fully implicit strong Itô-Taylor numerical methods for stochastic differential equations
Recommended article: ON EXACT CONVERGENCE RATE OF STRONG NUMERICAL SCHEMES FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Recommended article: Expansion of the global error for numerical schemes solving stochastic differential equations
Recommended article: Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients
Recommended article: Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations
description: scientific article; zbMATH DE number 2117870