A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

3 Citationer (Scopus)

Resumé

The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations and it is shown that the produced sequences converge almost surely. This is an improvement of the general result for SDEs with discontinuous drift, i.e. that the Euler-Maruyama approximations converge in probability to a strong solution of the SDE. A numerical example is presented together with a confidence interval for the numerical solutions.
OriginalsprogEngelsk
TitelAmerican Control Conference (ACC), 2014
Antal sider6
ForlagIEEE Press
Publikationsdato2014
Sider5180 - 5185
ISBN (Trykt)978-1-4799-3272-6
DOI
StatusUdgivet - 2014
Begivenhed2014 American Control Conference (ACC) - Portland, OR, USA
Varighed: 4 jun. 20146 jun. 2014

Konference

Konference2014 American Control Conference (ACC)
LandUSA
ByPortland, OR
Periode04/06/201406/06/2014
NavnAmerican Control Conference
ISSN0743-1619

Fingerprint

Euler-Maruyama Method
Convergence Results
Stochastic Equations
Differential equation
Converge
Strong Solution
Confidence interval
Euler
Rate of Convergence
Numerical Solution
Numerical Simulation
Numerical Examples
Approximation

Citer dette

@inproceedings{60ecb0c2469b4aa588e1bc3222f96575,
title = "A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift",
abstract = "The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations and it is shown that the produced sequences converge almost surely. This is an improvement of the general result for SDEs with discontinuous drift, i.e. that the Euler-Maruyama approximations converge in probability to a strong solution of the SDE. A numerical example is presented together with a confidence interval for the numerical solutions.",
author = "Maria Simonsen and Henrik Schi{\o}ler and John-Josef Leth and Horia Cornean",
year = "2014",
doi = "10.1109/ACC.2014.6859208",
language = "English",
isbn = "978-1-4799-3272-6",
series = "American Control Conference",
publisher = "IEEE Press",
pages = "5180 -- 5185",
booktitle = "American Control Conference (ACC), 2014",

}

Simonsen, M, Schiøler, H, Leth, J-J & Cornean, H 2014, A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift. i American Control Conference (ACC), 2014. IEEE Press, American Control Conference, s. 5180 - 5185, Portland, OR, USA, 04/06/2014. https://doi.org/10.1109/ACC.2014.6859208

A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift. / Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef; Cornean, Horia.

American Control Conference (ACC), 2014. IEEE Press, 2014. s. 5180 - 5185 (American Control Conference).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

TY - GEN

T1 - A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift

AU - Simonsen, Maria

AU - Schiøler, Henrik

AU - Leth, John-Josef

AU - Cornean, Horia

PY - 2014

Y1 - 2014

N2 - The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations and it is shown that the produced sequences converge almost surely. This is an improvement of the general result for SDEs with discontinuous drift, i.e. that the Euler-Maruyama approximations converge in probability to a strong solution of the SDE. A numerical example is presented together with a confidence interval for the numerical solutions.

AB - The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations and it is shown that the produced sequences converge almost surely. This is an improvement of the general result for SDEs with discontinuous drift, i.e. that the Euler-Maruyama approximations converge in probability to a strong solution of the SDE. A numerical example is presented together with a confidence interval for the numerical solutions.

U2 - 10.1109/ACC.2014.6859208

DO - 10.1109/ACC.2014.6859208

M3 - Article in proceeding

SN - 978-1-4799-3272-6

T3 - American Control Conference

SP - 5180

EP - 5185

BT - American Control Conference (ACC), 2014

PB - IEEE Press

ER -