This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that the vanilla maximum likelihood estimator (without regularization) is able to estimate the interaction potential parameter with optimal rate of convergence simultaneously in mean-field limit and in long-time dynamics. This to some extend avoids the curse-of-dimensionality for estimating large dynamical systems under symmetry of the particle interaction.
- Interacting particle systems
- Maximum likelihood estimation
- Mean-field regime
- Stochastic Vlasov equation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty