We consider a process X^$\epsilon$ solution of a stochastic Volterra equation with an unknown parameter $\theta$ in the drift function. The Volterra kernel is singular and given by K(u) = cu $\alpha$-1 __u>0 with $\alpha$ $\in$ (1/2, 1) and it is assumed that the diffusion coefficient is proportional to $\epsilon$ $\rightarrow$ 0 Based on the observation of a discrete sampling with mesh h $\rightarrow$ 0 of the Volterra process, we build a Quasi Maximum Likelihood Estimator. The main step is to assess the error arising in the reconstruction of the path of a semi-martingale from the inversion of the Volterra kernel. We show that this error decreases as h^{1/2} whatever is the value of $\alpha$. Then, we can introduce an explicit contrast function, which yields an efficient estimator when $\epsilon$ $\rightarrow$ 0.

翻译：我们考虑一个随机Volterra方程的解X^$\epsilon$，其漂移函数包含未知参数$\theta$。Volterra核具有奇异性，由K(u) = cu^{$\alpha$-1}1_{u>0}给出，其中$\alpha$ $\in$ (1/2, 1)，并假设扩散系数与趋于零的$\epsilon$成比例。基于对网格宽度h $\rightarrow$ 0的Volterra过程离散采样的观测，我们构建了一个拟极大似然估计量。关键步骤在于评估通过Volterra核反演重构半鞅路径时产生的误差。我们证明无论$\alpha$取何值，该误差均以h^{1/2}的速率衰减。随后，我们引入一个显式的对比函数，当$\epsilon$ $\rightarrow$ 0时，该函数可导出有效的估计量。