Mathématique
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Item Estimation et tests dans les processus de diffusion à dérive non régulière(2025) Djebbour, Khadîdja; BALASKA, LamiaMany natural, economic, and biological phenomena involve random fluctuations that cannot be captured by purely deterministic models. Stochastic differential equations (SDEs) provide a suitable framework by combining drift and diffusion components. This thesis focuses on a diffusion process with proportional delay and non-regular drift. Two main objectives are addressed: estimating the delay parameter via maximum likelihood in the small-diffusion regime, and constructing a simple versus simple parametric test based on the likelihood ratio. Theoretical results, inspired by the works of Ibragimov, Has’minskii, and Kutoyants, are supported by numerical simulations.Item Théorème de Girsanov et Applications(2025) Slimani, fatima zahra; Messabihi, AichaThis thesis explores Girsanov's Theorem and its applications in stochastic processes, focusing on the Ornstein-Uhlenbeck (O-U) process and Itô-Lévy processes. The study begins with foundational concepts of stochastic processes, including Brownian motion, martingales, and Itô calculus. It then rigorously presents Girsanov’s Theorem, which allows changing the probability measure to transform a stochastic process with drift into a driftless one (or vice versa). The applications demonstrate how Girsanov’s Theorem simplifies the analysis of O- U processes (used in finance and physics) and Itô-Lévy processes (incorporating jumps). Simulations in R illustrate the theoretical results, highlighting the theorem’s utility in financial modeling and risk-neutral pricing.Item Les Séries Stationnaires Appliquées(2025) BOUCHETA, Anissa; BENNAFLA, DjamilaThis thesis aims to study stationary time series, with a particular focus on their properties, identification, modelling, and forecasting. Emphasis will be placed on the application of these methods in specific domains. The project will include a practical analysis of real-world data and an implementation using R.Item Analyse d’un réseau de file d’attente sous des disciplines de service avec priorité(2025) Yekhlef, Hadjer; SAKHI, HananeIn this work, we study the stabilization of a queueing network model under service disciplines with priority; a multi-class fluid queueing system with priority consisting of N stations (N ≥ 3) and 2N classes (each station accommodates two classes). We base our stability analysis on the fluid model.Item Prévision des Séries Chronologiques à l’aide de la Régression Linéaire(2025) OURRAG, Nourhane Keltoum; BENNAFLA, DjamilaThis thesis explores the use of linear regression for time series forecasting. We analyze real-world time series data and implement linear regression techniques to predict future values. We pay special attention to data analysis, model diagnostics, and the evaluation of predictive performance. We also include practical examples and simulations using R, enabling the reader to understand the concepts and apply the presented methods.Item COMPORTEMENT ASYMPTOTIQUE D’UN MODÈLE D’HÉROÏNE AVEC LE TRAITEMENT ÂGE(2020) GASMI, Hadjira; BENTOUT, SoufianeItem ANALYSE MATHÉMATIQUE D’UN MODÈLE ÉPIDÉMIOLOGIQUE(2020) SELLAK, selima; BOUKHALFA, FatemaItem Existence de Solutions pour un Probleme Non Lineaire d’une Equation Differentielle Fractionnaire Implicite(2020) TAHRAOUI, Safaâ; Mami, Tawfiq FawziThe main objective of this paper is to study the existence of solutions for a nonlinear problem of an implicit fractional differential equation. The derivatives considered are in the sense of Caputo and of order between 0 and 1 in a Banach space with boundary conditions and in the second case with non-local ones. These results were obtained by applying the fixed point theory. Examples are included to illustrate the applicability of theoretical results.Item ÉTUDE DE BIFURCATION APPLIQUÉE AUX MODÈLES MATHÉMATIQUES EN SCIENCES(2020) BELOUADI, Khadidja Maroua; BELATTAR, ZokhaThe objective of this thesis is the theoretical and qualitative study of mathematical models applied to science, using some type of bifurcation, we are interested in examining the bifurcation P-A-H and bifurcation cusp theoretically.Item Equations différentirlles d’ordre fractionnaire sur les échelles de temps(2020) BERRAFA, HANANE; LADRANI, Fatima ZohraItem QUELQUES PROBLÈMES DE CAUCHY POUR LES ÉQUATIONS DIFFÉRENTIELLES NON-LINÉAIRES(2020) BOUBOSSELA, Wassila; BIROUD, Kheir eddineIn this memory,we focus on the existence of solution for a nonlinear boundary problem of third and fourth differential equations using the method of upper and lower solutions and some fixed point theorems like Larey Schauder theorem and Guo-Krasnosel’skii and expansion of cones. .Item Fonctions presque périodiques et équations différentielles(2020) raoui, fatna; TCHOUAR, FatimaItem CALCUL rFRACTIONNAIRE CONFORMABLE SUR LES ÉCHELLES DE TEMPS(2020)In this memory , we introduce the definition of nabla conformable fractional derivative of order 2]0; 1] and their important properties , we introduce and develop the notion of nabla conformable fractional integral of order 2]0; 1] on time scales . The basic tools for fractional differentiation and fractional integration are then developed . The Hilger time scale calculus is obtained as a particular case , by choosing = 1 . Many basic properties of the theory are proved .Item DÉRIVATION FRACTIONNAIRE APPLIQUÉE À L’ÉTUDE DE DEUX PROBLÈMES DIFFÉRENTIELS FRACTIONNAIRES NON-LINÉAIRES(2020) MEGTAITI, Sihem; HAMMOUDI, AhmedThe principle of fractional derivation has many applications. It intervenes in the resolution of several nonlinear fractional problems in particular, in the study of existence and uniqueness. This paper discusses different appliquations of this principle as well as some of its extensions and generalizations that involve in the resolution of nonlinear fractional differential problems.We demonstrate the existence and uniqueness of solutions using the principle of Banach contactions and the fixed point theorems of Schaefer and Kranoselskii.Item CALCUL FRACTIONNAIRE(2020) ALI, ZAHIRA; BENAISSA, AbdelkaderItem Les équations différentielles semi linéaires avec retard à domaine non dense(2020) Mekhalfi, Kheira; Mekhalfi, KheiraItem Oscillation d’une équation différentielle d’ordre n dans les échelles de temps(2020) GANIAR, MOUAFAK; Beniani, AbderrahmaneItem Dérivée d'ordre fractionnaire de Grunwald-Letnikov(2023) YAHIAOUI YOUCEFI, Asya; MEKHALF, KheiraThe work presented in this memory is part of the framework of adapting with fractional calculus by introducing the fractional integration and fractional di erentiation linear operators of Riemann-Liouville and Gr unwald-Letnikov. Particular attention is devoted to the auxiliary tools necessary to de ne these new concepts as certain special functions (Gamma-b^eta...) and to the Laplace transform technique. Then, we present the de nitions of fractional derivatives in the sens of Riemann- Liouville and Gr unwald-Letnikov. Also, we present some basic properties of di erintegrals, such as linearity, the Leibniz rule and composition. Finally, we explain the links between these derivativesItem Problèmes de Cauchy dans l’espace des distributions(2023) Taharaoui, Romaissae; TCHOUAR, Fatima ZahraThis work is devoted to the study of the Cauchy problem within the context of the distribution space. We have explored integrable and regular functions that hold values in a Banach space. Furthermore, we have tackled the concept of distribution semi-groups. In conclusion, we have examined the necessary conditions for the Cauchy problem to be well-posed in the distribution space.Item Inverse de Drazin et ses applications(2023) Slaimi, Hanane; Hariri, MohamedLe mémoire présenté est une contribution à la théoire des matrices carrées et de l’inverse généralisé de Drazin des opérateurs linéaires et son application sur des systèmes différentiels implicites. Ce mémoire comporte une introduction et quatre chapitres et une liste bibliographique de dix neuf titres.