Least squares estimation for path-distribution dependent stochastic differential equations

We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter $\epsilon>0$. The estimator, based on $n$ (where $n\in\mathbb{N}$) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as $\epsilon \to 0$ and $n \to \infty$. This indicates that the least squares estimator obtained is consistent with the true value. Moreover, we obtain the rate of convergence and derive the asymptotic distribution of least squares estimator