Least squares estimation for path-distribution dependent stochastic differential equations

Abstract: 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 greater than zero. The estimator, based on n discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as epsilon goes to zero and n goes to infinity. 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.