In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution of the process and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval $[0, T]$, we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step ($\Delta_n$) and the number of particles ($N$) satisfy $\Delta_n \rightarrow 0$ and $N \rightarrow \infty$, and asymptotically normal when additionally the condition $\Delta_n N \rightarrow 0$ holds.

翻译：本文研究了随机McKean-Vlasov方程及其相关相互作用粒子系统的漂移系数与扩散系数的联合参数估计问题。分析在一般框架下展开，其中两个系数均依赖于过程解及其解本身的分布。基于固定区间$[0, T]$上相互作用粒子系统的离散观测，我们提出了一种基于伪似然方法的对比函数。研究表明，当离散化步长($\Delta_n$)与粒子数($N$)满足$\Delta_n \rightarrow 0$且$N \rightarrow \infty$时，对应的估计量具有相合性；若额外满足条件$\Delta_n N \rightarrow 0$，则估计量具有渐近正态性。