Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift

Abstract : We consider an Euler-Maruyama type approximation method for a stochastic differential equation (SDE) with a non-regular drift and regular diffusion coefficient. The method regu-larizes the drift coefficient within a certain class of functions and then the Euler-Maruyama scheme for the regularized scheme is used as an approximation. This methodology gives two errors. The first one is the error of regularization of the drift coefficient within a given class of parametrized functions. The second one is the error of the regularized Euler-Maruyama scheme. After an optimization procedure with respect to the parameters we obtain various rates, which improve other known results.
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Arturo Kohatsu-Higa, Antoine Lejay, Kazuhiro Yasuda. Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift. Journal of Computational and Applied Mathematics, Elsevier, 2017, 326C, pp.138-158. ⟨10.1016/j.cam.2017.05.015⟩. ⟨hal-00840211v5⟩

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