Berry-Esseen bounds for drift parameter estimation of discretely observed fractional Vasicek-type process

Fares Alazemi^a, Soukaina Douissi^b, Khalifa Es-Sebaiy<sup>a

a</sup> Department of Mathematics, Faculty of Science, Kuwait University, Kuwait
^b Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

Abstract: In this paper, we study statistical estimation problems of drift parameters of Vasicek-type processes driven by fractional Brownian motion. Based on fixed-time-step observations and using Malliavin calculus combined with the recent Nourdin-Peccati analysis, we provide estimators of the drift parameters and analyze their asymptotic behaviors. More precisely, we study the strong consistency and the asymptotic distribution of the estimators and we give the rate of their convergence in law.

Keywords: Parameter estimation, Vasicek-type process, fractional Brownian motion, Malliavin Calculus, Central limit theorems, Nourdin-Peccati analysis.

MSC: 60G15; 60G22; 62F12; 62M09; 62M86.

Language: English