Least squares estimation for path-distribution dependent stochastic differential equations

摘要

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 ε>0. The estimator, based on n (where n∈N) discrete time observations of the stochastic differential equation, is shown to be convergent weakly to the true value as ε→0 and n→∞. 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.