Weak approximation errors for stochastic differential equations with non-regular drift
Résumé
We consider an Euler-Maruyama type approximation method for a stochastic differential equation (SDE) with a
discontinuous drift and regular diffusion coefficient.
The method regularizes 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 is the error of regularization of the drift coefficient within a given class of parametrized functions and the second is the error of the regularized Euler-Maruyama scheme.
After an optimization procedure with respect to this parameter we obtain various rates, which improve other known results.
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