Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process

Abstract

In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.