{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:41:38Z","timestamp":1760139698953,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T00:00:00Z","timestamp":1650758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by dxt=\u03b8(\u03bc\u2212xt)dt+dStH, with \u03b8&gt;0, \u03bc\u2208R being unknown and t\u22650; here, SH represents a sub-fractional Brownian motion (sfBm). We introduce new estimators \u03b8^ for \u03b8 and \u03bc^ for \u03bc based on discrete time observations and use techniques from Nordin\u2013Peccati analysis. For the proposed estimators \u03b8^ and \u03bc^, 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.<\/jats:p>","DOI":"10.3390\/e24050594","type":"journal-article","created":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T22:22:41Z","timestamp":1650838961000},"page":"594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1606-7835","authenticated-orcid":false,"given":"Anas D.","family":"Khalaf","sequence":"first","affiliation":[{"name":"General Directorate of Education in Saladin, Ministry of Education, Tikrit 34001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0170-5286","authenticated-orcid":false,"given":"Tareq","family":"Saeed","sequence":"additional","affiliation":[{"name":"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"}]},{"given":"Reman","family":"Abu-Shanab","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, University of Bahrain, Sakhir P.O. Box 32038, Bahrain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4497-1362","authenticated-orcid":false,"given":"Waleed","family":"Almutiry","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9026-5632","authenticated-orcid":false,"given":"Mahmoud","family":"Abouagwa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.jkss.2015.12.001","article-title":"Least squares estimator for non\u2013ergodic Ornstein\u2013Uhlenbeck processes driven by Gaussian processes","volume":"45","author":"Ouknine","year":"2016","journal-title":"J. Korean Stat. 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