| Abstract: |
| In this talk we will establish a central limit theorem for the Euler-Maruyama scheme approximating multidimensional SDEs with elliptic Brownian diffusion, under very mild regularity requirements on the drift coefficients.
When the drift is H\older continuous, we show that the limiting law of the rescaled fluctuations around the true solution is characterised by the solution of a hybrid Young-It\^o differential equation. When the drift has positive Sobolev regularity, this limit is characterised by the solution of a transformed SDE.
Our result is an extension of the result of Jacod--Protter (1998) in which SDEs with bounded differentiable coefficients were considered. To compensate for the lack of regularity of the drifts, we utilize the regularization effect from the non-degenerate noise. |
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