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

By Thomas Muller-Gronbach, Larisa Yaroslavtseva. Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2018

61 citations recorded by the source corpus.

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 $p\in [1,\infty)$ as in the case of SDEs with Lipschitz coefficients.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/9751ce00474c92a9e95f094a65a5c4701af79af2

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Citations in the corpus

• The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem (2019, methodology): “Lower bounds will be also addressed in a forthcoming work by Müller-Gronbach and Yaroslavtseva.”