Central limit theorem and Cramér-type moderate deviations for Milstein scheme
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912626328469504 |
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| author | Chen, Peng Jiang, Hui Wang, Jing |
| author_facet | Chen, Peng Jiang, Hui Wang, Jing |
| contents | 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 $π_η$. Subsequently, we derive both normalized and self-normalized Cramér-type moderate deviations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Central limit theorem and Cramér-type moderate deviations for Milstein scheme Chen, Peng Jiang, Hui Wang, Jing Probability 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 $π_η$. Subsequently, we derive both normalized and self-normalized Cramér-type moderate deviations. |
| title | Central limit theorem and Cramér-type moderate deviations for Milstein scheme |
| topic | Probability |
| url | https://arxiv.org/abs/2510.03053 |