Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

DOI10.1007/S00211-017-0903-9zbMATH Open1432.65012DBLPjournals/nm/LeobacherS18arXiv1610.07047OpenAlexW2544214212WikidataQ47555841 ScholiaQ47555841MaRDI QIDQ1692306

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Publication date: 26 January 2018

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Abstract: We prove strong convergence of order $1/4-epsilon$ for arbitrarily small $epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.

Full work available at URL: https://arxiv.org/abs/1610.07047

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