Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process
Anas D. Khalaf,
Tareq Saeed,
Reman Abu-Shanab,
Waleed Almutiry,
Mahmoud Abouagwa
Affiliations
Anas D. Khalaf
General Directorate of Education in Saladin, Ministry of Education, Tikrit 34001, Iraq
Tareq Saeed
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Reman Abu-Shanab
Mathematics Department, College of Science, University of Bahrain, Sakhir P.O. Box 32038, Bahrain
Waleed Almutiry
Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia
Mahmoud Abouagwa
Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
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.
