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：---- 估计离散观测的相互作用粒子系统的参数 研究论文摘要： 本文研究随机McKean-Vlasov方程的漂移和扩散系数以及相应粒子系统的联合参数估计问题。由于两种系数均与过程的解和解的分布有关，所以我们提出了一种基于伪似然方法的对比函数。我们从相互作用的粒子系统在固定时间间隔$[0,T]$内的离散观测出发。我们证明了当离散化步长($\Delta_n$)和粒子数($N$)满足$\Delta_n\rightarrow 0$和$N\rightarrow \infty$时，相关的估计量是一致的，并且当附加条件$\Delta_n N\rightarrow 0$时渐近正常的。