First order strong approximations of scalar SDEs defined in a domain
type: Item
instance of: scholarly article
title: First order strong approximations of scalar SDEs defined in a domain
zbMATH Open document ID: 1306.60075
author: A. Neuenkirch
author: Lukasz Szpruch
published in: Numerische Mathematik
publication date: 2014-09-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.0390
review text: In order to generate strong approximate solutions of stochastic differential equations (SDEs) of the form \[ dy(t)= a(y(t))\,dt+ b(y(t))\,dw(t) \] with coefficients that are not Lipschitz, a Lamperti-type transformation is applied to the SDE to obtain an SDE of the form \[ dx(t)= f(x(t))\,dt+\lambda dw(t), \] whose solution is approximated using a backward Euler-Maruyama method (BEM). The inverse transform of this approximate solution yields an approximate solution of the original SDE. Under certain conditions, strong convergence of order 1 of the BEM approximate solution of the transformed SDE is proved. Strong convergence of order 1 of the approximate solution of the original SDE is established for five well-known SDEs that arise in mathematical finance and biomathematics.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C30
zbMATH DE Number: 6341754
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Lamperti-type transformation
zbMATH Keywords: backward Euler-Maruyama method
describes a project that uses: sde
MaRDI profile type: Publication
OpenAlex ID: W2011337807
arXiv ID: 1209.0390
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DOI: 10.1007/S00211-014-0606-4
description: scientific article