Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

Understand

We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles.

• We study two cases: one in which we observe multiple independent trajectories of the McKean-Vlasov SDE, and another in which we observe multiple particles from the interacting particle system.
• In each case, we begin by establishing consistency and asymptotic normality of the (approximate) offline maximum likelihood estimator, in the limit as the number of observations $N\rightarrow\infty$.
• We then propose an online maximum likelihood estimator, which is based on a continuous-time stochastic gradient ascent scheme with respect to the asymptotic log-likelihood of the interacting particle system.