Measuring the irreversibility of numerical schemes for reversible stochastic differential equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.65007
author: Markos Katsoulakis
author: Yannis Pantazis
author: Luc Rey-Bellet
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.5665
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 6357679
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: detailed balance
zbMATH Keywords: reversibility
zbMATH Keywords: relative entropy
zbMATH Keywords: entropy production
zbMATH Keywords: numerical integration
zbMATH Keywords: (overdamped) Langevin process
zbMATH Keywords: Euler-Maruyama method
zbMATH Keywords: Milstein method
MaRDI profile type: Publication
OpenAlex ID: W3099747197
Wikidata QID: Q57453408
arXiv ID: 1207.5665
DOI: 10.1051/M2AN/2013142
title: Measuring the irreversibility of numerical schemes for reversible stochastic differential equations
published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
review text: The entropy production rate (EPR) is used to estimate the loss of reversibility when approximations of the solution of a reversible stochastic differential equation are generated using a numerical method. This analysis is applied to the overdamped Langevin equation to determine that the explicit Euler-Maruyama method yields order \(\Delta t^2\) decrease of the EPR in the case of additive noise, but the EPR is not reduced by reducing the stepsize \(\Delta t\) in the case of multiplicative noise.NEWLINENEWLINE However, the explicit Milstein method is shown to yield order \(\Delta t\) decrease in the EPR in the case of multiplicative noise. The BBK integrator is shown to yield order \(\Delta t\) decrease in the EPR when applied to a Langevin system with additive noise.
reviewed by: Melvin D. Lax
description: scientific article; zbMATH DE number 6357679