Parameter estimation of discretely observed interacting particle systems

We consider the problem of joint parameter estimation for drift and volatility 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 ($\Delta_n$) goes to 0 and the number of particles N goes to $\infty$, and asymptotically normal when additionally the condition $\Delta_n N \rightarrow 0$ holds. We will also compare our results (and our condition on the decay of the discretization step) with the results known for classical SDEs.

The talk is based on a joint work with A. Heidari, V. Pilipauskaite and M. Podolskij.

Zoom link: https://univr.zoom.us/j/81227077465