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 intro...

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Detalles Bibliográficos
Autores principales: Khalaf, Anas D., Saeed, Tareq, Abu-Shanab, Reman, Almutiry, Waleed, Abouagwa, Mahmoud
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Review
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9142111/
https://www.ncbi.nlm.nih.gov/pubmed/35626479
http://dx.doi.org/10.3390/e24050594
Descripción
Sumario: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.

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