[1] Istas J, Lang G. Quadratic variations and estimation of the local Hölder index of a gaussian process. Ann Inst H Poincaré Probab Stat, 1997, 33(4):407-436 [2] Kubilius K, Mishura Y.The rate of convergence of Hurst index estimate for the stochastic differential equation. Stochastic Processes and their Applications, 2012, 122(11):3718-3739 [3] Kutoyants Y A. Statistical Inference for Ergodic Diffusion Processes. Springer, 2004 [4] Liptser R S, Shiryaev A N. Statistics of Random Processes:Ⅱ Applications. Second Ed. Applications of Mathematics. Springer, 2001 [5] Kleptsyna M L, Le Breton A. Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Stat Inference Stoch Process, 2002, 5:229-248 [6] Tudor C, Viens F. Statistical aspects of the fractional stochastic calculus. Ann Statist, 2007, 35(3):1183-1212 [7] Bercu B, Coutin L, Savy N. Sharp large deviations for the fractional Ornstein-Uhlenbeck process. Theory Probab Appl, 2011, 55(4):575-610 [8] Brouste A, Kleptsyna M. Asymptotic properties of MLE for partially observed fractional diffusion system. Stat Inference Stoch Process, 2010, 13(1):1-13 [9] Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat Probab Lett, 2010, 80(11/12):1030-1038 [10] Hu Y, Nualart D, Zhou H. Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter. Stat Inference Stoch Process, 2019, 22:111-142 [11] Basawa I V, Scott D J. Asymptotic Optimal Inference for Non-ergodic Models. Lecture Notes in Statistics 17. New York:Springer, 1983 [12] Dietz H M, Kutoyants Y A. Parameter estimation for some non-recurrent solutions of SDE. Statistics and Decisions, 2003, 21(1):29-46 [13] Belfadli R, Es-Sebaiy K, Ouknine Y. Parameter estimation for fractional Ornstein-Uhlenbeck processes:Non-ergodic case. Front Sci Eng Int J Hassan Ⅱ Acad Sci Technol, 2011, 1(1):1-16 [14] El Machkouri M, Es-Sebaiy K, Ouknine Y. Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes. J Korean Stat Soc, 2016, 45:329-341 [15] Mendy I. Parametric estimation for sub-fractional Ornstein-Uhlenbeck process. Journal of Statistical Planning and Inference, 2013, 143(4):663-674 [16] Diedhiou A, Manga C, Mendy I. Parametric estimation for SDEs with additive sub-fractional Brownian motion. Journal of Numerical Mathematics and Stochastics, 2011, 3(1):37-45 [17] Sottinen T, Viitasaari L. Parameter estimation for the Langevin equation with stationary-increment Gaussian noise. Stat Inference Stoch Process, 2018, 21(3):569-601 [18] Cai C, Xiao W. Parameter estimation for mixed sub-fractional Ornstein-Uhlenbeck process. arXiv:1809.02038v2 [19] Sghir A. The generalized sub-fractional Brownian motion. Communications on Stochastic Analysis, 2013, 7(3):Article 2 [20] Jolis M. On the Wiener integral with respect to the fractional Brownian motion on an interval. J Math Anal Appl, 2007, 330:1115-1127 [21] Nualart D. The Malliavin calculus and related topics. Second edition. Springer, 2006 [22] Nourdin I, Peccati G. Normal approximations with Malliavin calculus:from Stein's method to universality. Cambridge University Press, 2012 [23] Nualart D, Peccati G. Central limit theorems for sequences of multiple stochastic integrals. Ann Probab, 2005, 33(1):177-193 [24] Kim Y T, Park H S. Optimal Berry-Esséen bound for statistical estimations and its application to SPDE. Journal of Multivariate Analysis, 2017, 155:284-304 [25] Chen Y, Hu Y, Wang Z. Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise. ALEA Lat Am J Probab Math Stat, 2017, 14:613-629 [26] Chen Y, Kuang N H, Li Y. Berry-Esséen bound for the Parameter Estimation of Fractional OrnsteinUhlenbeck Processes. Stoch Dyn, 2020, 20(1) [27] Billingsley P. Probability and measure. Third edition. A Wiley-Interscience Publication. New York:John Wiley & Sons, Inc, 1995 |