Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by [Formula: see text] , with [Formula: see text] , [Formula: see text] being unknown and [Formula: see text]; here, [Formula: see text] represents a sub-fractional Brownian motion (sfBm). We introduce new estimators [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] based on discrete time observations and use techniques from Nordin–Peccati analysis. For the proposed estimators [Formula: see text] and [Formula: see text] , strong consistency and the asymptotic normality were established by employing the properties of [Formula: see text]. Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H.