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Propriétés théoriques et applications en statistique et en simulation de processus et de champs aléatoires stationnaires

Abstract : This PhD thesis studies theorical and asymptotic properties of processes and random fields with some applications in statistics and simulation. A first part (Chapter 2, 3 and 4) is devoted to the construction of new models of random fields with a random error, expressed in term of Bernoulli shifts and to give some results about their limit theory. Weak dependence conditions used are proved to be more general than the well known notions such as strong mixing or association. We will study in this part the weak and strong invariance principle, for the random fields of interest. The second part of this thesis will be devoted to study estimation and simulation's problems with two kinds of dependence contexts. In Chapter 5, we first consider the question of texture simulations, with a non parametric resampling scheme for strong mixing random fields. The Chapter 6 is devoted to the construction and the parametric estimation of a new integer valued ARCH time serie. The existence result uses contraction arguments etablished in the first part for random fields and the asymptotic behaviour of parameters estimators, obtained using the (Gaussian) Quasi Maximum Likelihood Estimator (QMLE), is etablished with martingal differences type arguments. Finally, in Chapter 7, we introduce a new estimation procedure for Markovian ARCH models. The principle of this method is to smooth the Gaussian QML. We apply this method to the parametric estimation of LARCH type processes, for which the small values of the conditional variance make dificult to apply the usual QMLE technique.
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Contributor : Lionel Truquet <>
Submitted on : Wednesday, March 4, 2009 - 12:23:17 PM
Last modification on : Sunday, January 19, 2020 - 6:38:29 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 8:30:06 PM


  • HAL Id : tel-00365716, version 1



Lionel Truquet. Propriétés théoriques et applications en statistique et en simulation de processus et de champs aléatoires stationnaires. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2008. Français. ⟨tel-00365716⟩



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