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Central limit theorem and Cram\'{e}r-type moderate deviations for Milstein scheme
Peng Chen, Hui Jiang, Jing Wang
https://arxiv.org/abs/2510.03053 https://

Central limit theorem and Cramér-type moderate deviations for Milstein scheme
In this paper, we investigate the Milstein numerical scheme with step size $η$ for a stochastic differential equation driven by multiplicative Brownian motion. Under some appropriate coefficient conditions, the continuous-time system and its discrete Milstein scheme approximation each possess unique invariant measures, which we denote by $π$ and $π_η$ respectively. We first establish a central limit theorem for the empirical measure $Π_η$, a statistical consistent estimator of $π_η$. Su…