The Euler scheme with irregular coefficients

By Liqing Yan. 2002

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On the constructions of the skew Brownian motion (2007, methodology): “The question of the simulation of the solution of some SDE with discontinuous diffusion coefficients is a problem which have been hardly treated (See however [45, 16, 93]).”
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2009, unknown): “In contrast to our results on superlinearly growing coeﬃcients, Yan (2002) proves numerically weak convergence of the Euler scheme if both drift and diﬀusion function have at most linear growth.”
On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients (2015, methodology): “The strong rates of the Euler-Maruyama approximation for SDEs with Hölder continuous diffusion coefficient were first established in [29, 6, 13].”
Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients (2016, methodology): “2 in [25], plays a crucial role in our argument.”