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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 3, Pages 502–525
DOI: https://doi.org/10.4213/tvp5238 (Mi tvp5238) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

F. Alazemia, S. Douissib, Kh. Es-Sebaiya

a Department of Mathematics, Faculty of Science, Kuwait University, Kuwait
b Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco
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DOI: https://doi.org/10.4213/tvp5238
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
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 3, Pages 401–420
DOI: https://doi.org/10.1137/S0040585X97T98957X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 502–525; Theory Probab. Appl., 64:3 (2019), 401–420
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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