This article is cited in 3 papers

Berry–Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process with discrete observations

F. Alazemi^a, S. Douissi^b, Kh. 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 the problem of estimating the drift of mixed fractional Ornstein–Uhlenbeck processes with fixed-time-step observations. Using Malliavin calculus and the recent Nourdin–Peccati analysis, we analyze the asymptotic behavior of the estimator. More precisely, we study the strong consistency and the asymptotic distribution of the estimator, and we also provide the rate of its convergence in law for all $H\in (0,1)$. Moreover, we prove that the estimator satisfies an almost sure central limit theorem for all $H\in (0,{3}/{4}]$.

Keywords: parameter estimation, mixed Ornstein–Uhlenbeck process, central limit theorem, Nourdin–Peccati analysis, almost sure central limit theorem.

Received: 25.06.2018
Revised: 14.02.2019

DOI: 10.4213/tvp5238

 English version: Theory of Probability and its Applications, 2019, 64:3, 401–420

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