Parameter Estimation In The Non-stationary Ornstein-uhlenbeck Process With Linear Drift

Ornstein–Uhlenbeck (O-U) process is an important diffusion process. Recently, it is widelyused in describing the connections between branching process and Lévy process, the stochasticvolatilities of finance assets, and the default intensities. In reality, when the price of financialinstruments or goods deviate from its long term equilibrium level substantially, the price has atendency to its long term equilibrium level. If the price motion follows the O-U process, thecontrolling parameter of the O-U process would draw the price back to its long term level. Theprocess has more backward trend than general stochastic process which is in accord with the facts.In this paper, we consider the parameter estimators for the non-stationary O-U process withlinear drift. First, we introduce the maximum likelihood estimators(MLE) and the trajectory fittingestimators(TFE) for the unknown parameters in the linear drift. Then by splitting techniques,martingale limit theory, we have studied the asymptotic behaviors of the two types of estimators,including the law of iterated logarithm and the asymptotic distribution.