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

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Abstrakt

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

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