Exact Maximum Likelihood Estimator for Drift Fractional Brownian Motion at Discrete Observation by Yaozhong Hu

This paper deals with the problems of consistence and strong consistence of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. A central limit theorem for these estimators is also obtained by using the Malliavin calculus. 1. Introduction. Long memory processes have been widely applied to various fields, such as finance, hydrology, network traffic analysis and so on. Fractional Brownian motions are one special class of long memory processes when the Hurst parameter H > 1/2. The stochastic calculus for these processes has now been well-established (see [2]). When a long memory model is used to describe some phenomena, it is important to identify the parameters in the model. In this paper, we shall consider the following simple model