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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.27225 |
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| _version_ | 1866915793609949184 |
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| author | Song, Ke Ling, Chengcheng Wang, Haiyi |
| author_facet | Song, Ke Ling, Chengcheng Wang, Haiyi |
| contents | We study a singular stochastic equation driven by a regular noise of fractional Brownian type with Hurst index $H \in (1,\infty)\setminus\mathbb{Z}$ and drift coefficient $b \in \mathcal{C}^α$, where $α> 1 - \frac{1}{2H}$. The strong well-posedness of this equation was first established in [Ger23], a phenomenon referred to as regularization by regular noise. In this note, we provide a corresponding numerical analysis. Specifically, we show that the Euler-Maruyama approximation $X^n$ converges strongly to the unique solution $X$ with rate $n^{-1}$. Furthermore, under the additional assumption $b \in \mathcal{C}^1$, we show that $n(X - X^n)$ converges to a non-trivial limit as $n \to \infty$, thereby confirming that the rate $n^{-1}$ is in fact optimal upper bound for this scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization by regular noise: a numerical result Song, Ke Ling, Chengcheng Wang, Haiyi Probability We study a singular stochastic equation driven by a regular noise of fractional Brownian type with Hurst index $H \in (1,\infty)\setminus\mathbb{Z}$ and drift coefficient $b \in \mathcal{C}^α$, where $α> 1 - \frac{1}{2H}$. The strong well-posedness of this equation was first established in [Ger23], a phenomenon referred to as regularization by regular noise. In this note, we provide a corresponding numerical analysis. Specifically, we show that the Euler-Maruyama approximation $X^n$ converges strongly to the unique solution $X$ with rate $n^{-1}$. Furthermore, under the additional assumption $b \in \mathcal{C}^1$, we show that $n(X - X^n)$ converges to a non-trivial limit as $n \to \infty$, thereby confirming that the rate $n^{-1}$ is in fact optimal upper bound for this scheme. |
| title | Regularization by regular noise: a numerical result |
| topic | Probability |
| url | https://arxiv.org/abs/2510.27225 |