Geodesic
Berry–Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process with discrete observations
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 502-525 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Berry{\textendash}Esseen bounds and {ASCLTs} for drift parameter estimator of mixed fractional {Ornstein{\textendash}Uhlenbeck} process with discrete observations},
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F. Alazemi; S. Douissi; Kh. Es-Sebaiy. Berry–Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process with discrete observations. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 502-525. http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a4/

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