Publications

53. Khalifa Es-Sebaiy, Fares Alazemi. New Kolmogorov bounds in the CLT for random ratios and applications. Chaos, Solitons & Fractals, Volume 181, April 2024, 114686 (2024)

52. Khalifa Es-Sebaiy, Fares Alazemi, Mishari Al-Foraih. Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency. J Inequal Appl 2023, 62 (2023). https://doi.org/10.1186/s13660-023-02976-4

51. Maoudo Faramba Balde, Rachid Belfadli, Khalifa Es-Sebaiy. Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes. Stochastics and Dynamics. Vol. 23, No. 04, 2350029 (2023), DOI: https://doi.org/10.1142/S0219493723500296 

50. Belfadli, R., Es-Sebaiy, K. & Farah, FE. Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind. J Theor Probab 36, 3 (2023). https://doi.org/10.1007/s10959-023-01238-9

49. Soukaina Douissi, Khalifa Es-Sebaiy, Frederi G. Viens (2022). Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths: a Wiener chaos approach. Electron. J. Statist. 16(1): 3176-3211 (2022). DOI: 10.1214/22-EJS2021

 48. Rachid Belfadli, Khalifa Es-Sebaiy, Fatima-Ezzahra Farah (2022). Statistical analysis of the  non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean. Metrika: https://doi.org/10.1007/s00184-021-00854-x

47.  Khalifa Es-Sebaiy  (2022), Gaussian and hermite Ornstein–Uhlenbeck processes, Stochastic Analysis and Applications. https://doi.org/10.1080/07362994.2021.2022495

46. Soukaina Douissi, Khalifa Es-Sebaiy, George Kerchev, Ivan Nourdin. Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency, Electron. J. Statist. 16(1): 636-670 (2022). DOI: 10.1214/21-EJS1967

45. Khalifa Es-Sebaiy, Mishari Al-Foraih, Fares Alazemi. Wasserstein Bounds in the CLT of the MLE for the Drift Coefficient of a Stochastic Partial Differential Equation. Fractal and Fractional. 2021; 5(4):187.  https://doi.org/10.3390/fractalfract5040187

44. Abdulaziz Alsenafi, Mishari Al-Foraih, Khalifa Es-Sebaiy. Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters[J]. AIMS Mathematics, 2021, 6(11): 12780-12794. doi: 10.3934/math.2021738

43. Es-Sebaiy, Khalifa; Moustaaid, Jabrane; and Ouassou, Idir (2021) "Berry-Esseen Bounds for Approximate Maximum Likelihood Estimators in the α-Brownian Bridge," Journal of Stochastic Analysis: Vol. 2 : No. 2 , Article 8. DOI: 10.31390/josa.2.2.08 

42. Maoudo Faramba Baldé, Khalifa Es-Sebaiy, Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind, Modern Stoch. Theory Appl.(2021), 1-19, DOI 10.15559/21-VMSTA179

41. Khalifa Es-Sebaiy, Mishari Al-Foraih, Fares Alazemi, Statistical inference for nonergodic weighted fractional Vasicek models, Modern Stoch. Theory Appl.(2021), 1-17, DOI 10.15559/21-VMSTA176

40. Khalifa Es-Sebaiy, Jabrane Moustaaid (2021). Optimal Berry-Esséen bound for Maximum likelihood estimation of the drift parameter in α-Brownian bridge, Journal of the Korean Statistical Society 50:403–418 https://doi.org/10.1007/s42952-020-00084-3 

39. Soukaina Douissi , Khalifa Es-Sebaiy and Soufiane Moussaten. Asymptotics of the cross-variation of Young integrals with respect to a general self-similar Gaussian process. Acta Mathematica Scientia, 2020, 40(6): 1941–1960, https://doi.org/10.1007/s10473-020-0621-8

38. Khalifa Es-Sebaiy, Mohammed Es.Sebaiy. Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model, Statistical Methods & Applications, (2020).  https://doi.org/10.1007/s10260-020-00528-4 

37. Soukaina Douissi, Khalifa Es-Sebaiy, Fatimah Alshahrani and Frederi Viens.  AR(1) processes driven by second-chaos white noise: Berry-Esséen bounds for quadratic variation and parameter estimation, 2020,   Stochastic Processes and their Applications, in press.

36. Fares Alazemi, Abdulaziz Alsenafi and Khalifa Es-Sebaiy. Parameter estimation for Gaussian mean-reverting Ornstein-Uhlenbeck processes of the second kind: non-ergodic case, Stochastics and Dynamics Vol. 20, No. 2 (2020)  (25 pages) DOI: 10.1142/S0219493720500112

35. Khalifa Es-Sebaiy, Fatima-Ezzahra Farah and Astrid Hilbert. Weyl Multifractional Ornstein-Uhlenbeck Processes Mixed with a Gamma Distribution,  2020, Probability and Mathematical Statistics. http://www.math.uni.wroc.pl/~pms/files_doi/f1744/f1744.pdf  

34. Soukaina Douissi, Khalifa Es-Sebaiy  and Ciprian A. Tudor. Hermite Ornstein-Uhlenbeck processes mixed with a Gamma distribution, 2020, Publicationes Mathematicae Debrecen, 96(1-2):1-22. http://publi.math.unideb.hu/contents.php .

33. Maoudo Faramba Balde,  Khalifa Es-Sebaiy  and Ciprian A. Tudor. Ergodicity  and  drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process of the second kind.  Applied Mathematics and Optimization,  81, 785–814 (2020). https://doi.org/10.1007/s00245-018-9519-4 

32. Salwa Bajja, Khalifa Es-Sebaiy, Lauri Viitasaari. Volatility estimation in fractional Ornstein-Uhlenbeck models.  Stochastic Models, Volume 36, 2020 - Issue 1, Pages 94-111, https://doi.org/10.1080/15326349.2019.1692668.

31. Fares Alazemi, Soukaina Douissi and Khalifa Es-Sebaiy. Berry-Esséen bounds for drift parameter estimation of discretely observed  fractional Vasicek-type process, Theory of Stochastic Processes, Vol. 24 (40), no. 1, 2019, pp. 6–18.

30. Soukaina Douissi, Khalifa Es-Sebaiy, Frederi G. Viens. Berry-Esséen bounds for parameter estimation of general Gaussian processes (2019).  ALEA, Lat. Am. J. Probab. Math. Stat. 16, 633–664 (2019) DOI: 10.30757/ALEA.v16-23 

29. Fares Alazemi, Soukaina Douissi and Khalifa 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 of Probability and its Applications (TVP)). http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=5238&option_lang=eng

28. Azzouz Dermoune, Khalifa Es-Sebaiy, Mohammed Es.Sebaiy, Jabrane Moustaaid. Parametrizations, weights, and optimal prediction (2021).  Communications in Statistics-Theory and Methods, 50(4), 815-836.  https://www.tandfonline.com/doi/full/10.1080/03610926.2019.1642489

27. Khalifa Es-Sebaiy, Fares Alazemi, Mishari Al-Foraih. Least squares type estimation for discretely observed non-ergodic Gaussian Ornstein-Uhlenbeck processes. Acta Mathematica Scientia, 2019,  Volume 39, Issue 4, pp 989–1002.

26. Fares Alazemi, Khalifa Es-Sebaiy, Youssef Ouknine. Efficient and superefficient estimators of filtered Poisson process intensities. Communications in Statistics- Theory and Methods, Volume 48, 2019 - Issue 7 

25. Khalifa Es-Sebaiy, Frederi G. Viens. Optimal rates for parameter estimation of stationary Gaussian processes.  Stochastic Processes and their Applications, Volume 129, Issue 9, September 2019, Pages 3018-3054. https://doi.org/10.1016/j.spa.2018.08.010   

24.  Brahim El Onsy,  Khalifa Es-Sebaiy, and Djibril Ndiaye. Parameter estimation for  discretely observed non-ergodic fractional Ornstein-Uhlenbeck processes of the second kind. Brazilian Journal of Probability and Statistics 2018, Vol. 32, No. 3, 545-558.

23. Salwa Bajja, Khalifa Es-Sebaiy, Lauri Viitasaari. Limit theorems for quadratic variations of the Lei-Nualart process. Springer Proceedings in Mathematics & Statistics, Stochastic Processes and Applications, SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. https://link.springer.com/chapter/10.1007/978-3-030-02825-1_5 

22. Salwa Bajja, Khalifa Es-Sebaiy, Lauri Viitasaari. Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean. J. Korean Statist. Soc. 46 (2017), no. 4, 608--622.

21.  Brahim El Onsy,  Khalifa Es-Sebaiy and Ciprian Tudor. Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process of the second kind. Commun. Stoch. Anal. 11 (2017), no. 2, 119-136. 

20.  Brahim El Onsy,  Khalifa Es-Sebaiy, Frederi Viens. Parameter Estimation for a partially observed Ornstein-Uhlenbeck process with long-memory noise. Stochastics, Volume 89 (2017) - Issue 2, Pages: 431-468.

19. Mohamed El Machkouri, Khalifa Es-Sebaiy and Idir Ouassou. On local linear regression for strongly mixing random fields. Journal of Multivariate Analysis 156 (2017): 103-115.

18. Ahmed, S. E., Es-Sebaiy, K., Hussein, A., Ouassou, I., & Snowdon, A. (2016, June). An Efficient Estimation Strategy in Autoregressive Conditional Poisson Model with Applications to Hospital Emergency Department Data. In International Workshop on Matrices and Statistics (pp. 177-190). Springer, Cham. 

17. Soufiane Aazizi and Khalifa Es-Sebaiy. Berry-Esséen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion.  Random Oper. Stoch. Equ. (2016); 24 (1):1-13.

16. Mohamed El Machkouri, Khalifa Es-Sebaiy, Youssef Ouknine. Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes.   Journal of the Korean Statistical Society 45 (2016) 329-341.

15.  Khalifa Es-Sebaiy and Ciprian Tudor. Fractional Ornstein-Uhlenbeck processes mixed with a Gamma distribution", FRACTALS 23(03):10 PAGES, 2015.

14. Khalifa Es-Sebaiy and Djibril Ndiaye. On drift estimation for non-ergodic fractional Ornstein-Uhlenbeck process with discrete observations. Afr. Stat. 9 (2014), 615–625.

13.  Peggy Cénac and Khalifa Es-Sebaiy. Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes,  Probability and Mathematical Statistics, Vol. 35, Fasc. 2 (2015), pp. 285–300.

12. Khalifa Es-Sebaiy. Berry-Esséen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes. Statistics and Probability Letters 83 (2013) 2372–2385.

11. Rachid Belfadli, Khalifa Es-Sebaiy and Youssef Ouknine . Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-Ergodic Case. Frontiers in Science and Engineering (An InternationalJournal Edited by Hassan II Academy of Science and Technology). 1, no. 1, (2011) 1-16..

10. Khalifa Es-Sebaiy, Ivan Nourdin. Parameter estimation for \alpha-fractional bridges (2013). F. Viens et al (eds), Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart, Springer Proceedings in Mathematics and Statistics 34, 385-412.

9. Xavier Bardina, Khalifa Es-Sebaiy. AN EXTENSION OF BIFRACTIONAL BROWNIAN MOTION. Communications on Stochastic Analysis, Vol. 5, No. 2 (2011) 333-340.

8. Xavier Bardina, Khalifa Es-Sebaiy and Ciprian A. Tudor. Approximation of the finite dimensional distributions of multiple fractional integrals. Journal of Mathematical Analysis and Applications. Volume 369, Issue 2, 2010, Pages 694-711

7. Khalifa Es-Sebaiy and Youssef Ouknine. Mutual Information for Stochastic Differential Equations Driven by Fractional Brownian Motion. Random Operators / Stochastic Eqs. 18 (2010), 1-9.

6. Khalifa Es-Sebaiy and Ciprian A. Tudor. Non-central limit theorem for the cubic variation of a class of selfsimilar stochastic processes, 2010, Theory of Probability and its Applications, 55:3 (2010), 507–529.

5. Khalifa Es-Sebaiy, David Nualart, Youssef Ouknine and Ciprian A. Tudor. Occupation densities for certain processes related to fractional Brownian motion. Stochastics, Vol. 82, No. 2, April 2010, 133–147.

4. Khalifa Es-Sebaiy, Idir Ouassou and Youssef Ouknine. Estimation of the drift of fractional Brownian motion. Statistics and Probability Letters 79, 2009, 1647-1653.

3. Khalifa Es-Sebaiy and Youssef Ouknine. How rich is the class of processes which are infinitely divisible with respect to time ?, Statistics and Probability Letters. Vol. 78, 2008, pp. 537-547.

2. Khalifa Es-Sebaiy and Ciprian A. Tudor. Lévy processes and Itô-Skorohod integrals. Theory of Stochastic Processes, Vol. 14 (30), no. 2, 2008, pp. 10-18.

1. Khalifa Es-Sebaiy and Ciprian A. Tudor. Multidimentional bifractional Brownian motion : Itô and Tanaka formulas, Stochastic and Dynamics, Vol. 7 (3), 2007 pp. 365-388.