We consider the problem of parameter estimation for a McKean stochastic differential equation, and the associated system of weakly interacting particles. The problem is motivated by many applications in areas such as neuroscience, social sciences (opinion dynamics, cooperative behaviours), financial mathematics, statistical physics. We will first survey some model properties related to propagation of chaos and ergodicity and then move on to discuss the problem of parameter estimation both in offline and on-line settings. In the on-line case, we propose an online estimator, which evolves according to a continuous-time stochastic gradient descent algorithm on the asymptotic log-likelihood of the interacting particle system. The talk will present our convergence results and then show some numerical results for two examples, a linear mean field model and a stochastic opinion dynamics model. This is joint work with Louis Sharrock, Panos Parpas and Greg Pavliotis. Preprint: https://arxiv.org/abs/2106.13751
