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Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process
Anas D Khalaf1, Tareq Saeed2, Reman Abu-Shanab3
1General Directorate of Education in Saladin, Ministry of Education, Tikrit 34001, Iraq.
Abstract:
This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by dxt=θ(μ−xt)dt+dStH, with θ>0, μ∈R being unknown and t≥0; here, SH represents a sub-fractional Brownian motion (sfBm). We introduce new estimators θ^ for θ and μ^ for μ based on discrete time observations and use techniques from Nordin−Peccati analysis. For the proposed estimators θ^ and μ^, strong consistency and the asymptotic normality were established by employing the properties of SH. Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H.
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