Deterministic quadrature formulas for SDEs based on simplified weak Itô-Taylor steps
type: Item
instance of: scholarly article
title: Deterministic quadrature formulas for SDEs based on simplified weak Itô-Taylor steps
zbMATH Open document ID: 1382.65023
author: Thomas Müller-Gronbach
author: Larisa Yaroslavtseva
published in: Foundations of Computational Mathematics
publication date: 2017-03-17T00:00:00Z
review text: A deterministic algorithm for the weak approximation of the solution of a stochastic differential equation (SDE) is constructed. For the time-stepping, a simplified weak order \(\gamma\) Ito-Taylor method is used. After every time step, the diameter and cardinality of the support of the discrete measure are reduced to avoid an explosion of the computational cost. Under suitable smoothness assumptions on the coefficients of the SDE, the resulting algorithm yields the optimal rate of convergence of the error in terms of complexity, i.e., \(r/d\), where \(d\) is the dimensionality of the problem and the payoff function has bounded derivatives up to order \(r\). Results of numerical simulations in one space dimension are given. In higher space dimensions, however, the support cardinality reduction step becomes computationally expensive. Hence it is not clear whether the algorithm as written in the paper can be practically employed for \(d\geq 2\).
reviewed by: Philipp Dörsek
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 6695908
zbMATH Keywords: quadrature
zbMATH Keywords: simplified weak Itô-Taylor step
zbMATH Keywords: lower bounds
zbMATH Keywords: optimal algorithms
zbMATH Keywords: numerical example
zbMATH Keywords: deterministic algorithm
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: s10208-015-9277-5
OpenAlex ID: W1190414567
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DOI: 10.1007/S10208-015-9277-5
description: scientific article; zbMATH DE number 6695908