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arXiv · 1610.07047

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

Gunther Leobacher·Michaela Szölgyenyi
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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.

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Gunther Leobacher, Michaela Szölgyenyi. 2016-10-22. Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. https://doi.org/10.1007/s00211-017-0903-9

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