TY - JOUR A1 - Lalaoui Ben Cherif, Sidi Mohamed A1 - Balatif, Omar A1 - Kebiri, Omar T1 - Analysis and optimal control of a vaccinated pandemic COVID-19 model JF - Journal of Mathematical Sciences Y1 - 2024 U6 - https://doi.org/10.1007/s10958-024-06992-7 SN - 1072-3374 VL - 280 IS - 4 SP - 582 EP - 604 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Kebiri, Omar A1 - Neureither, Lara A1 - Hartmann, Carsten T1 - Singularly Perturbed Forward-Backward Stochastic Differential Equations: Application to the Optimal Control of Bilinear Systems T2 - Computation Y1 - 2018 U6 - https://doi.org/10.3390/computation6030041 SN - 2079-3197 VL - 6 IS - 3 SP - 41 EP - 41 ER - TY - GEN A1 - Hartmann, Carsten A1 - Kebiri, Omar A1 - Neureither, Lara A1 - Richter, Lorenz T1 - Variational approach to rare event simulation using least-squares regression T2 - Chaos: An Interdisciplinary Journal of Nonlinear Science Y1 - 2019 U6 - https://doi.org/10.1063/1.5090271 SN - 1089-7682 SN - 1054-1500 VL - 29 IS - 6 ER - TY - GEN A1 - Mezdoud, Zaineb A1 - Hartmann, Carsten A1 - Remita, Mohamed Riad A1 - Kebiri, Omar T1 - α-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs T2 - Bulletin of the Institute of Mathematics Academia Sinica : New series Y1 - 2021 U6 - https://doi.org/10.21915/BIMAS.2021304 SN - 2304-7909 SN - 2304-7895 VL - 16 IS - 3 SP - 263 EP - 288 ER - TY - GEN A1 - Redjil, Amel A1 - Gherbal, H. B. A1 - Kebiri, Omar T1 - Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps T2 - Stochastic Analysis and Applications Y1 - 2021 U6 - https://doi.org/10.1080/07362994.2021.1991809 SN - 1532-9356 VL - Vol. 41 (2023) IS - 1 SP - 115 EP - 133 ER - TY - GEN A1 - Kebiri, Omar A1 - Hafida, Bouanani A1 - Abdeldjebbar, Kandouci T1 - On the existence and uniqueness of solutions to forward backward stochastic differential equations driven by G-Brownian motion T2 - Bulletin of the Institute of Mathematics Academia Sinica : New series Y1 - 2020 SN - 2304-7909 SN - 2304-7895 VL - 15 SP - 217 EP - 236 ER - TY - GEN A1 - Eddahbi, Mhamed A1 - Kebiri, Omar A1 - Sene, Abou T1 - Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients T2 - Axioms N2 - In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the Itô–Krylov’s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts. KW - quadratic backward stochastic differential equations KW - infinite time horizon KW - Zvonkin transformation KW - Itô–Krylov’s type formula KW - quadratic partial differential equation KW - epidemic models KW - stochastic control Y1 - 2023 U6 - https://doi.org/10.3390/axioms12121068 SN - 2075-1680 VL - 12 IS - 12 ER - TY - JOUR A1 - Grid, Maroua A1 - Agram, Nacira A1 - Kebiri, Omar A1 - Øksendal, Bernt T1 - Deep learning for solving initial path optimization of mean-field systems with memory JF - Stochastics Y1 - 2024 U6 - https://doi.org/10.1080/17442508.2024.2402741 SN - 1744-2508 SP - 1 EP - 22 PB - Informa UK Limited ER - TY - JOUR A1 - Bouguetof, Khaoula A1 - Mezdoud, Zaineb A1 - Kebiri, Omar A1 - Hartmann, Carsten T1 - On the existence and uniqueness of the solution to multifractional stochastic delay differential equation JF - Fractional Calculus and Applied Analysis N2 - AbstractIn this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results. Y1 - 2024 U6 - https://doi.org/10.1007/s13540-024-00314-z SN - 1311-0454 VL - 27 IS - 5 SP - 2284 EP - 2304 PB - Springer Science and Business Media LLC ER - TY - JOUR A1 - Bouanani, Hafida A1 - Kebiri, Omar A1 - Hartmann, Carsten A1 - Redjil, Amel T1 - Optimal Relaxed Control for a Decoupled G-FBSDE JF - Journal of Optimization Theory and Applications N2 - AbstractIn this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit. Y1 - 2024 U6 - https://doi.org/10.1007/s10957-024-02495-2 SN - 0022-3239 VL - 202 IS - 3 SP - 1027 EP - 1059 PB - Springer Science and Business Media LLC ER - TY - JOUR A1 - Boumezbeur, Zakaria A1 - Boutabia, Hacène A1 - Redjil, Amel A1 - Kebiri, Omar T1 - Differentiability of G-neutral stochastic differential equations with respect to parameter JF - Random Operators and Stochastic Equations N2 - In this paper, we study the differentiability of solutions of neutral stochastic differential equations driven by G-Brownian motion with respect to parameter. Under suitable assumptions, we show that solutions are differentiable with respect to the parameter which appears in the initial data. In addition, the stochastic differential equation of the derivative is given and the existence-uniqueness of solution is proved. Moreover, an example to illustrate the theoretically obtained results is presented. Y1 - 2024 U6 - https://doi.org//10.1515/rose-2024-2005 SN - 0926-6364 VL - 32 IS - 2 SP - 159 EP - 173 PB - Walter de Gruyter GmbH ER - TY - GEN A1 - Siddiqui, Maryam A1 - Eddahbi, Mhamed A1 - Kebiri, Omar T1 - Numerical solutions of stochastic differential equations with jumps and measurable drifts T2 - Mathematics N2 - This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 12. Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example. Y1 - 2023 U6 - https://doi.org/10.3390/math11173755 SN - 2227-7390 VL - 11 IS - 17 SP - 1 EP - 14 PB - MDPI AG ER - TY - GEN A1 - Belili, Mohamed Cherif A1 - Sahari, Mohamed Lamine A1 - Kebiri, Omar A1 - Zeghdoudi, Halim T1 - Analyzing bifurcations and optimal control strategies in SIRS epidemic models: insights from theory and COVID-19 data T2 - Mathematical and Computational Applications N2 - This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread. KW - flip bifurcation KW - transcritical bifurcation KW - bifurcation curve KW - discrete epidemic model KW - stability KW - numerical simulation KW - optimal control Y1 - 2024 U6 - https://doi.org/10.3390/mca29040069 SN - 2297-8747 VL - 29 IS - 4 PB - MDPI ER - TY - GEN A1 - Saci, Akram A1 - Redjil, Amel A1 - Boutabia, Hacene A1 - Kebiri, Omar T1 - Fractional stochastic differential equations driven by G-Brownian motion with delays T2 - Probability and Mathematical Statistics Y1 - 2023 U6 - https://doi.org/10.37190/0208-4147.00092 SN - 0208-4147 VL - 43 IS - 1 SP - 1 EP - 21 ER - TY - GEN A1 - Ben Gherbal, Hanane A1 - Redjil, Amel A1 - Kebiri, Omar T1 - The relaxed maximum principle for G-stochastic control systems with controlled jumps T2 - Advances in Mathematics: Scientific Journal Y1 - 2022 U6 - https://doi.org/10.37418/amsj.11.12.11 SN - 1857-8365 VL - 11 IS - 12 SP - 1313 EP - 1343 ER -