| Abstract: |
| We study a singular stochastic equation driven by regular noise of fractional Brownian type with Hurst index $H \in (1,\infty)\setminus\mathbb{Z}$ and drift coefficient $b \in \mathcal{C}^\alpha$, where $\alpha > 1 - \tfrac{1}{2H}$. The strong well-posedness of this equation was first established in [Gerencs\`er, 23], a phenomenon known as {\it regularization by regular noise}. In this note, we provide a numerical analysis of the equation. Specifically, we prove that the Euler--Maruyama approximation $X^n$ converges strongly to the unique solution $X$ at rate $n^{-1}$. Moreover, we show that $n(X - X^n)$ converges in probability to a non-trivial limit as $n \to \infty$, which confirms that the rate $n^{-1}$ is optimal for this scheme. In this sense, this provides a first-order numerical method for equations with non-Lipschitz drift while still achieving the rate $n^{-1}$. |
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