Parameter estimation of discretely observed interacting particle systems

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 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 (Δ_n) and the number of particles ( N) satisfy Δ_n→0 and N→∞, and asymptotically normal when additionally the condition Δ_nN→0 holds.