Contributions à la modélisation de la dépendance stochastique

Abstract : In this thesis, we study the modeling of stochastic dependence for random vectors from the copula viewpoint. The first part is a numerical exploration of the notions of copulas and dependence measures in the context of uncertainty modeling for numerical simulation. The second part focus on the Nataf and Rosenblatt transformations. We show that the Nataf transformation reduces to an hypothesis of Gaussian copula for the random vector, which allows us to generalize this transformation to any absolutely continuous distribution with arbitrary elliptical copula. In the gaussian case, we show the equality between the Nataf and Rosenblatt transformations. The third part is dedicated to dependence modeling under constraint. We characterize the joint distribution of order statistics in terms of marginal distributions and copulas, and we construct a new family of copulas dedicated to this setting. We show the existence and unicity of a maximal element in this family. The fourth part focus on discrete models, for which their is no one-to-one relation between joint distribution functions and copulas. We propose an innovative algorithm to compute rectangular probabilities for a large class of such distributions, which is much faster, more accurate and less memory consuming than any other existing algorithms.
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Submitted on : Tuesday, December 3, 2013 - 8:49:35 PM
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Régis Lebrun. Contributions à la modélisation de la dépendance stochastique. Probabilités [math.PR]. Université Paris-Diderot - Paris VII, 2013. Français. ⟨NNT : 20908922⟩. ⟨tel-00913510⟩

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