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

Arturo Kohatsu-Higa (1) , Antoine Lejay (2, 3) , Kazuhiro Yasuda (4)

1 Department of Mathematical Sciences, Ritsumeikan Universtiy
2 TOSCA - TO Simulate and CAlibrate stochastic models
3 IECL - Institut Élie Cartan de Lorraine
4 NTT Secure Platform Laboratories [Tokyo]

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.

Keywords: Stochastic differential equation; Euler-Maruyama scheme; discontinuous drift; weak; rate of convergence; Malliavin calculus

Domains: Probability [math.PR]

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, 2017, 326C, pp.138-158. ⟨10.1016/j.cam.2017.05.015⟩. ⟨hal-00840211v5⟩