L’objet de cette thèse est d’étudier la probabilité de survie d’un processus de branchement en environnement aléatoire markovien et d’étendre dans ce cadre les résultats connus en milieu aléatoire i.i.d.. le cœur de l’étude repose sur l’utilisation des théorèmes limites locaux pour une marche aléatoire centrée (Sn)n≥0 sur R à pas markoviens et pour (rnn)n≥0, où mn = min (0, S1,... , Sn). Pour traiter le cas d’un environnement aléatoire markovien, nous développons dans un premier temps une étude des théorèmes locaux pour une chaîne semi-markovienne à valeurs réelles en améliorant certains résultats déjà connus et développés initialement par E. L. Presman (voir aussi [21]). Nous utilisons ensuite ces résultats pour l’étude du comportement asymptotique de la probabilité de survie d’un processus de branchement critique en environnement aléatoire markovien. Les résultats principaux de cette thèse (théorème limite local et son application au processus de branchement critique eu milieu aléatoire) ont été acceptés et publiés dans le Comptes Rendus de l‘Académie des Sciences ([20]). Le texte principal de cette mémoire de thèse consisite les détails des preuves. / The purpose of this thesis is to study the survival probability of a branching process in markovian random environment and expand in this framework some known results which have been developed for a branching processus in i.i.d. random environment, the core of the study is based on the use of the local limit theorem for a centered random walk (Sn)n≥o on R with markovian increasements and for (mn)n≥0. where mn = min (O. S1,……. , Sn). In order to treat the case of a markovian random environment, we establish firstly a local limit theorem for a semi-markovian chain on R. which improves certain results developed initially by E. P. Presman (see also [21]). And then we use these results to study the asymptotic behavior of a critical branching process in markovian environment. The main results et this thesis (local limit theorem and its application to the critical branching process in random environment) are accepted and published in Comptes Rendus de l’Académie des Sciences ([20]). The principal text et this thesis contains the details of the proofs.

The popularity of the wireless networks is so great that we will soon reach the point where most of the devices work based on that, but new challenges in wireless channel access will be created with these increasingly widespread wireless communications. Multi-channel CSMA protocols have been designed to enhance the throughput of the next generation wireless networks compared to single-channel protocols. However, their performance analysis still needs careful considerations. In this thesis, a set of techniques are proposed to model and analyse the CSMA protocols in terms of channel sensing and channel access. In that respect, the performance analysis of un-slotted multi-channel CSMA protocols is studied through considering the hidden terminals. In the modelling phase, important parameters such as shadowing and path loss impairments are being considered. Following that, due to the high importance of spectrum sensing in CSMA protocols, the Double-Threshold Energy Detector (DTED) is thoroughly investigated in this thesis. An iterative algorithm is also proposed to determine optimum values of detection parameters in a sensing-throughput problem formulation. Vehicle-to-Roadside (V2R) communication, as a part of Intelligent Transportation System (ITS), over multi-channel wireless networks is also modelled and analysed in this thesis. In this respect, through proposing a novel mathematical model, the connectivity level which an arbitrary vehicle experiences during its packet transmission with a RSU is also investigated.