Rozprawy doktorskie na temat „Systèmes stochastiques de fonctions itérées”
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Portefaix, Christophe. "Modélisation des signaux et des images par les attracteurs fractals de systèmes de fonctions itérées (IFS)". Angers, 2004. http://www.theses.fr/2004ANGE0026.
Pełny tekst źródłaRésumé en anglais
Daoudi, Khalid. "Généralisations des systèmes de fonctions itérées : applications au traitement du signal". Paris 9, 1996. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1996PA090078.
Pełny tekst źródłaDubarry, Blandine. "Comportement asymptotique des systèmes de fonctions itérées et applications aux chaines de Markov d'ordre variable". Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S114/document.
Pełny tekst źródłaThe purpose of this thesis is the study of the asymptotic behaviour of iterated function systems (IFS). In a first part, we will introduce the notions related to the study of such systems and we will remind different applications of IFS such as random walks on graphs or aperiodic tilings, random dynamical systems, proteins classification or else $q$-repeated measures. We will focus on two other applications : the chains of infinite order and the variable length Markov chains. We will give the main results in the literature concerning the study of invariant measures for IFS and those for the calculus of the Hausdorff dimension. The second part will be dedicated to the study of a class of iterated function systems (IFSs) with non-overlapping or just-touching contractions on closed real intervals and adapted piecewise constant transition probabilities. We give criteria for the existence and the uniqueness of an invariant probability measure for the IFSs and for the asymptotic stability of the system in terms of bounds of transition probabilities. Additionally, in case there exists a unique invariant measure and under some technical assumptions, we obtain its exact Hausdorff dimension as the ratio of the entropy over the Lyapunov exponent. This result extends the formula, established in the literature for continuous transition probabilities, to the case considered here of piecewise constant probabilities. The last part is dedicated to a special case of IFS : Variable Length Markov Chains (VLMC). We will show that under a weak non-nullness condition and continuity for the ultrametric distance of the transition probabilities, they admit a unique invariant measure which is attractive for the weak convergence
Boulanger, Christophe. "Stabilité et stabilisation de systèmes différentiels stochastiques". Metz, 1998. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1998/Boulanger.Christophe.SMZ9807.pdf.
Pełny tekst źródłaIn this study we study stability and stabilization of stochastic differential systems by using Lyapunov techniques developed by Khasminskii or Arnold. The first part deals with asymptotic stabilization in probability of stochastic differential systems. The output regulation and stabilization of nonlinear control stochastic systems is studied using locally bounded state feedback. Besides, necessary and sufficient conditions are established to asymptotically stabilize in probability controlled stochastic systems by means of output feedback laws. In the linear case, a linear output feedback law is used. For a class of stochastic differential systems whose output have a triangular structure, sufficient conditions are obtained to asymptotically stabilize in probability the system by means of a smooth output feedback integrator. In the second part, large-scale stochastic differential systems in hierarchical form are exponentially stabilized in mean square if only each of the subsustems is exponentially stable in mean square. Furthermore, composite stochastic differential systems with time delays, and cascade systems are stabilized. The goal of the third part is to compute sufficient conditions for a control of Lyapunov function associated with a class of controlled stochastic differential systems. The fourth part deals with stochastic differential systems driven bay an infinite dimensional Brownian motion. Some Lyapunov techniques are obtained to exponentially stabilize in mean square or asymptotically stabilize in probability this class of systems. Moreover, a nonlinear filtering problem with correlated noises, bounded coefficients and a signal evolving in an infinite dimensional space is studied. We derive the Kushner-Stratonovich and the Zakai equations
Kandji, Baye Matar. "Stochastic recurrent equations : structure, statistical inference, and financial applications". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAG004.
Pełny tekst źródłaWe are interested in the theoretical properties of Stochastic Recurrent Equations (SRE) and their applications in finance. These models are widely used in econometrics, including financial econometrics, to explain the dynamics of various processes such as the volatility of financial returns. However, the probability structure and statistical properties of these models are still not well understood, especially when the model is considered in infinite dimensions or driven by non-independent processes. These two features lead to significant difficulties in the theoretical study of these models. In this context, we aim to explore the existence of stationary solutions and the statistical and probabilistic properties of these solutions.We establish new properties on the trajectory of the stationary solution of SREs, which we use to study the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of GARCH-type (generalized autoregressive conditional heteroskedasticity) conditional volatility models. In particular, we study the stationarity and statistical inference of semi-strong GARCH(p,q) models where the innovation process is not necessarily independent. We establish the consistency of the QMLE of semi-strong GARCHs without assuming the commonly used condition that the stationary distribution admits a small-order moment. In addition, we are interested in the two-factor volatility GARCH models (GARCH-MIDAS); a long-run, and a short-run volatility. These models were recently introduced by Engle et al. (2013) and have the particularity to admit stationary solutions with heavy-tailed distributions. These models are now widely used but their statistical properties have not received much attention. We show the consistency and asymptotic normality of the QMLE of the GARCH-MIDAS models and provide various test procedures to evaluate the presence of long-run volatility in these models. We also illustrate our results with simulations and applications to real financial data.Finally, we extend a result of Kesten (1975) on the growth rate of additive sequences to superadditive processes. From this result, we derive generalizations of the contraction property of random matrices to products of stochastic operators. We use these results to establish necessary and sufficient conditions for the existence of stationary solutions of the affine case with positive coefficients of SREs in the space of continuous functions. This class of models includes most conditional volatility models, including functional GARCHs
De, Castro Gilles. "C*-algèbres associées à certains systèmes dynamiques et leurs états KMS". Phd thesis, Université d'Orléans, 2009. http://tel.archives-ouvertes.fr/tel-00541042.
Pełny tekst źródłaLiorit, Grégory. "Etude des valeurs propres de quelques processus matriciels à l'aide d'une méthode de Laplace pour des intégrales stochastiques itérées et de la formule de Campbell-Hausdorff stochastique". Poitiers, 2005. http://www.theses.fr/2005POIT2329.
Pełny tekst źródłaBroise, Anne. "Aspects stochastiques de certains systèmes dynamiques, transformations dilatantes de l'intervalle, fractions continues multidimensionnelles". Rennes 1, 1994. http://www.theses.fr/1994REN10034.
Pełny tekst źródłaDemni, Nizar. "Processus stochastiques matriciels, systèmes de racines et probabiltés non commutatives". Paris 6, 2007. https://tel.archives-ouvertes.fr/tel-00192155.
Pełny tekst źródłaDemni, Nizar. "Processus stochastiques matriciels, systèmes de racines et probabilités non commutatives". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00192155.
Pełny tekst źródłaAberkane, Samir. "Systèmes tolérants aux défauts : analyse et synthèse stochastique". Nancy 1, 2006. https://tel.archives-ouvertes.fr/tel-00151379.
Pełny tekst źródłaDespite the evident interaction between FDI and reconfiguration algorithms, it is true that the research on FDI and reconfiguration methods has often evolved separately, certainly because of the difficulty of each of these problems. The main contribution of this work is to use a mathematical model that includes in the same analysis framework the FDI and reconfiguration algorithms. Such a model belongs to the class of Markovian jump linear systems. In this class of systems, two random processes are defined: the first represents system components failures and the second represents the FDI process. The first problematic considered in this thesis is related to the synthesis of output feedback controllers that stochastically stabilize this class of systems subject to Brownian motion. The developed results are based essentially on Lyapunov theory and Supermartingale notion. The different synthesis conditions are formulated as nonlinear matrix inequalities problematic. Noncovex optimization algorithms were then proposed to solve these conditions. The second problematic addressed in this work concerns the multi-objective control of this class of Markovian jump systems. The specifications and objectives under consideration include stochastic stability, H2 and H∞ performances. Output feedback controllers synthesis conditions were also proposed in term of LMI, BMI and NLMI. Finally, we have addressed the discrete-time counterpart and proposed H2/H∞ synthesis conditions. The developed results were applied to the problematic of control of networked systems subject to delays, packet loss and failures
Wang, Xiao-Min. "Contribution à l'étude de la commande et du filtrage optimaux des systèmes implicites singuliers". Nice, 1988. http://www.theses.fr/1988NICE4235.
Pełny tekst źródłaJin, Xiong. "Construction et analyse multifractale de fonctions aléatoires et de leurs graphes". Phd thesis, Université Paris Sud - Paris XI, 2010. http://tel.archives-ouvertes.fr/tel-00841501.
Pełny tekst źródłaCastiel, Eyal. "Study of QB-CSMA algorithms". Thesis, Toulouse, ISAE, 2019. http://www.theses.fr/2019ESAE0038.
Pełny tekst źródłaPerformance of wireless networks, in which users share the air as support for their communications is strongly limited by electromagnetic interference. That is, two users close to each other trying to send a message on the same frequency will experience interference between their messages, eventually leading to the loss of some information. It is then crucial to develop medium access protocols aiming to limit the occurrence of such a phenomena by choosing in an effective (and distributed) manner which station is allowed to transmit. From a scientific point of view, it is a difficult issue which has had some attention from the community in the field of computer science and applied probability in the past 30 years. Recently, a new class of medium access protocols - called adaptive CSMA - emerged and seem quite promising: for example, it has been shown that they exhibit a desirable property: throughput optimality (maximum stability). The goal of this project is to increase the knowledge we have the adaptive CSMA (or CSMA QB, for Queue Based) which is to this day quite limited (notably in the expected waiting time of a request arriving in the system, called delay). Our goal will be to prove theoric results to enhance our understanding of the throughput/delay trade-off
Hammami, Sonia. "Sur la stabilisation de systèmes dynamiques continus non linéaires exploitant les matrices de formes en flèche : application à la synchronisation de systèmes chaotiques". Phd thesis, Ecole Centrale de Lille, 2009. http://tel.archives-ouvertes.fr/tel-00579521.
Pełny tekst źródłaVialard, François-Xavier. "APPROCHE HAMILTONIENNE POUR LES ESPACES DE FORMES DANS LE CADRE DES DIFFÉOMORPHISMES: DU PROBLÈME DE RECALAGE D'IMAGES DISCONTINUES À UN MODÈLE STOCHASTIQUE DE CROISSANCE DE FORMES". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2009. http://tel.archives-ouvertes.fr/tel-00400379.
Pełny tekst źródłaLe cas des images discontinues n'était compris que partiellement. La première contribution de ce travail est de traiter complètement le cas des images discontinues en considérant comme modèle d'image discontinues l'espace des fonctions à variations bornées. On apporte des outils techniques pour traiter les discontinuités dans le cadre d'appariement par difféomorphismes. Ces résultats sont appliqués à la formulation Hamiltonienne des géodésiques dans le cadre d'un nouveau modèle qui incorpore l'action d'un difféomorphisme sur les niveaux de grille de l'image pour prendre en compte un changement d'intensité. La seconde application permet d'étendre la théorie des métamorphoses développée par A.Trouvé et L.Younes aux fonctions discontinues. Il apparait que la géométrie de ces espaces est plus compliquée que pour des fonctions lisses.
La seconde partie de cette thèse aborde des aspects plus probabilistes du domaine. On étudie une perturbation stochastique du système Hamiltonien pour le cas de particules (ou landmarks). D'un point de vue physique, on peut interpréter cette perturbation comme des forces aléatoires agissant sur les particules. Il est donc naturel de considérer ce modèle comme un premier modèle de croissance de forme ou au moins d'évolutions aléatoires de formes.
On montre que les solutions n'explosent pas en temps fini presque sûrement et on étend ce modèle stochastique en dimension infinie sur un espace de Hilbert bien choisi (en quelque sorte un espace de Besov ou Sobolev sur une base de Haar). En dimension infinie la propriété précédente reste vraie et on obtient un important (aussi d'un point de vue numérique) résultat de convergence du cas des particules vers le cas de dimension infinie. Le cadre ainsi développé est suffisamment général pour être adaptable dans de nombreuses situations de modélisation.