Khalifa Es-Sebaiy
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Khalifa Es-Sebaiy has a total of 44 co-authors. Here are the top co-authors by number of shared publications:
- Fares Alazemi
Kuwait Univ, Fac Sci, Dept Math, Kuwait, Kuwait
7 shared publications - Youssef Ouknine
Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco
6 shared publications - Mishari Al-Foraih
Department of Mathematics, College of Science, Kuwait University, Safat, Kuwait
5 shared publications Fares Alazemi
4 shared publications- Abdulaziz Alsenafi
Kuwait Univ, Fac Sci, Dept Math, Kuwait, Kuwait
3 shared publications Brahim El Onsy
3 shared publications
Latest Publications
- Open Access
- 16 September 2026
- Published by Elsevier in Results in Applied Mathematics
- Vol. 32
Kolmogorov bounds for the maximum likelihood and method of moments estimators for the Vasicek interest rate model
- 16 September 2026
- Published by Elsevier in Results in Applied Mathematics
- Vol. 32
Open AccessKolmogorov bounds for the maximum likelihood and method of moments estimators for the Vasicek interest rate model
- Open Access
- 17 April 2026
- Published by Springer Nature in Journal of Inequalities and Applications
- Vol. 2026 (1)
A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals
- 17 April 2026
- Published by Springer Nature in Journal of Inequalities and Applications
- Vol. 2026 (1)
Open AccessA quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals
- Open Access
- 29 January 2026
- Published by Springer Nature in Advances in Continuous and Discrete Models
- Vol. 2026 (1)
Improved Berry-Esseen bounds for parameter estimation of a fractional Ornstein-Uhlenbeck process observed at high frequency
- 29 January 2026
- Published by Springer Nature in Advances in Continuous and Discrete Models
- Vol. 2026 (1)
Open AccessImproved Berry-Esseen bounds for parameter estimation of a fractional Ornstein-Uhlenbeck process observed at high frequency
- Open Access
- 8 January 2025
- Published by Elsevier in Results in Applied Mathematics
- Vol. 25
Kolmogorov bounds for drift parameter estimation of continuously-observed SPDEs
- 8 January 2025
- Published by Elsevier in Results in Applied Mathematics
- Vol. 25
Open AccessKolmogorov bounds for drift parameter estimation of continuously-observed SPDEs
- 1 March 2024
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 181
New Kolmogorov bounds in the CLT for random ratios and applications
- 1 March 2024
- Published by Elsevier in Chaos, Solitons & Fractals
- Vol. 181
New Kolmogorov bounds in the CLT for random ratios and applications
- Open Access
New Kolmogorov bounds in the CLT for random ratios and applications
We develop techniques for determining an explicit Berry-Esseen bound in the Kolmogorov distance for the normal approximation of a ratio of Gaussian functionals. We provide an upper bound in terms of the third and fourth cumulants, using some novel techniques and sharp estimates for cumulants. As applications, we study the rate of convergence of the distribution of discretized versions of minimum contrast and maximum likelihood estimators of the drift parameter of the Ornstein-Uhlenbeck process. Moreover, we derive upper bounds that are strictly sharper than those available in the literature.
Open AccessNew Kolmogorov bounds in the CLT for random ratios and applications
We develop techniques for determining an explicit Berry-Esseen bound in the Kolmogorov distance for the normal approximation of a ratio of Gaussian functionals. We provide an upper bound in terms of the third and fourth cumulants, using some novel techniques and sharp estimates for cumulants. As applications, we study the rate of convergence of the distribution of discretized versions of minimum contrast and maximum likelihood estimators of the drift parameter of the Ornstein-Uhlenbeck process. Moreover, we derive upper bounds that are strictly sharper than those available in the literature.
- Open Access
- 26 April 2023
- Published by Springer Nature in Journal of Inequalities and Applications
- Vol. 2023 (1) , 1-17
Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denotedθ, for the Ornstein-Uhlenbeck process $X := \{X_{t},t\geq 0\}$ observed at high frequency. We provide an approximate minimum contrast estimator and an approximate maximum likelihood estimator ofθ, namely $\widetilde{\theta}_{n}:= {1}/{ (\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2} )}$ , and $\widehat{\theta}_{n}:= -{\sum_{i=1}^{n} X_{t_{i-1}} (X_{t_{i}}-X_{t_{i-1}} )}/{ (\Delta _{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2} )}$ , respectively, where $t_{i} = i \Delta _{n}$ , $i=0,1,\ldots , n $ , $\Delta _{n}\rightarrow 0$ . We provide Wasserstein bounds in the central limit theorem for $\widetilde{\theta}_{n}$ and $\widehat{\theta}_{n}$ .- 26 April 2023
- Published by Springer Nature in Journal of Inequalities and Applications
- Vol. 2023 (1) , 1-17
Open AccessWasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denotedθ, for the Ornstein-Uhlenbeck process $X := \{X_{t},t\geq 0\}$ observed at high frequency. We provide an approximate minimum contrast estimator and an approximate maximum likelihood estimator ofθ, namely $\widetilde{\theta}_{n}:= {1}/{ (\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2} )}$ , and $\widehat{\theta}_{n}:= -{\sum_{i=1}^{n} X_{t_{i-1}} (X_{t_{i}}-X_{t_{i-1}} )}/{ (\Delta _{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2} )}$ , respectively, where $t_{i} = i \Delta _{n}$ , $i=0,1,\ldots , n $ , $\Delta _{n}\rightarrow 0$ . We provide Wasserstein bounds in the central limit theorem for $\widetilde{\theta}_{n}$ and $\widehat{\theta}_{n}$ . - 11 April 2023
- Published by World Scientific Pub Co Pte Ltd in Stochastics and Dynamics
- Vol. 23 (04)
Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes
In this paper, we consider the Ornstein–Uhlenbeck (OU) process defined as solution to the equation [ ], [ ], where [ ] is a Gaussian process with stationary increments, whereas [ ] is unknown parameter to be estimated. We provide an upper bound in Kolmogorov distance for normal approximation of the least squares estimator [ ] of the drift parameter [ ] on the basis of the continuous observation [ ], as [ ]. Our approach is based on some novel estimates involving a combination of Malliavin calculus and Stein’s method for normal approximation. We apply our result to fractional OU processes of the first kind, and improved the upper bound of the Kolmogorov distance for the LSE [ ] provided by [Y. Chen, N. Kuang and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes, Stoch. Dyn. 20(4) (2020) 2050023; Y. Chen and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes with the hurst parameter [ ], Commun. Stat. Theory Methods 50(13) (2021) 2996–3013], respectively, in the cases [ ] and [ ]. We also apply our approach to fractional OU processes of the second kind.
- 11 April 2023
- Published by World Scientific Pub Co Pte Ltd in Stochastics and Dynamics
- Vol. 23 (04)
Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes
In this paper, we consider the Ornstein–Uhlenbeck (OU) process defined as solution to the equation [ ], [ ], where [ ] is a Gaussian process with stationary increments, whereas [ ] is unknown parameter to be estimated. We provide an upper bound in Kolmogorov distance for normal approximation of the least squares estimator [ ] of the drift parameter [ ] on the basis of the continuous observation [ ], as [ ]. Our approach is based on some novel estimates involving a combination of Malliavin calculus and Stein’s method for normal approximation. We apply our result to fractional OU processes of the first kind, and improved the upper bound of the Kolmogorov distance for the LSE [ ] provided by [Y. Chen, N. Kuang and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes, Stoch. Dyn. 20(4) (2020) 2050023; Y. Chen and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes with the hurst parameter [ ], Commun. Stat. Theory Methods 50(13) (2021) 2996–3013], respectively, in the cases [ ] and [ ]. We also apply our approach to fractional OU processes of the second kind.
- 15 February 2023
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 37 (1) , 860-876
Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind
- 15 February 2023
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 37 (1) , 860-876
Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind
- Open Access
Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $\theta$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $\theta$, namely $\widetilde{\theta}_{n}\coloneqq {1}/{\left(\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$, and $\widehat{\theta}_{n}\coloneqq -{\sum_{i=1}^{n} X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(\Delta_{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i \Delta_{n}$, $ i=0,1,\ldots, n $, $\Delta_{n}\rightarrow 0$. We provide Wasserstein bounds in central limit theorem for $\widetilde{\theta}_{n}$ and $\widehat{\theta}_{n}$.Open AccessWasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $\theta$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $\theta$, namely $\widetilde{\theta}_{n}\coloneqq {1}/{\left(\frac{2}{n} \sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$, and $\widehat{\theta}_{n}\coloneqq -{\sum_{i=1}^{n} X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(\Delta_{n} \sum_{i=1}^{n} X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i \Delta_{n}$, $ i=0,1,\ldots, n $, $\Delta_{n}\rightarrow 0$. We provide Wasserstein bounds in central limit theorem for $\widetilde{\theta}_{n}$ and $\widehat{\theta}_{n}$.