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Rozprawy doktorskie na temat "Systèmes stochastiques de fonctions itérées"
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.
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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 źródłaCzęści książek na temat "Systèmes stochastiques de fonctions itérées"
"La compression d'images: les systèmes de fonctions itérées". W Springer Undergraduate Texts in Mathematics and Technology, 335–77. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-69213-5_11.
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