Parameter estimation in the models with long-range dependence

Abstract

We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic differential equations are constructed. It is proved that the estimators converge almost surely to the parameter value, as the observation interval expands and the interval between observations vanishes. A bound for the rate of convergence is given. As an auxiliary result of independent interest we establish global estimates for fractional derivative of fractional Brownian motion.