Parameter estimation of discretely observed interacting particle systems
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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 (Δ_n) and the number of particles (N) satisfy Δ_n → 0 and N →∞, and asymptotically normal when additionally the condition Δ_n N → 0 holds.
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