On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient

DOI10.1214/19-AIHP997zbMATH Open1494.65006arXiv1809.08423OpenAlexW3010883102MaRDI QIDQ2179625

Author name not available (Why is that?)

Publication date: 13 May 2020

Published in: (Search for Journal in Brave)

Abstract: Recently a lot of effort has been invested to analyze the $L_p$-error of the Euler-Maruyama scheme in the case of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space. For scalar SDEs with a piecewise Lipschitz drift coefficient and a Lipschitz diffusion coefficient that is non-zero at the discontinuity points of the drift coefficient so far only an $L_p$-error rate of at least $1/(2p)-$ has been proven. In the present paper we show that under the latter conditions on the coefficients of the SDE the Euler-Maruyama scheme in fact achieves an $L_p$-error rate of at least $1/2$ for all $pin[1,infty)$ as in the case of SDEs with Lipschitz coefficients.

Full work available at URL: https://arxiv.org/abs/1809.08423

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2179625)