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Modélisation et simulation de processus stochastiques non gaussiens

Abstract : The aim of this work is to construct an approximate model in order to simulate the paths of a non-Gaussian strictly stationary process given solely the one-dimensional marginal distribution, or the N-first statistical moments of this distribution, together with the autocorrelation function. The approach developped in this thesis is based on two well-known methods of Gaussian simulation: the spectral method and the markovianization one. Moreover, if only the N-first moments of the one-dimensional marginal distribution are given, the maximum entropy principle is used to choose this distribution. Given the one-dimensional marginal distribution, a non-linear transformation is constructed. This transformation is then projected on the basis of Hermite polynomials. The model yields a polynomial transformation of a standard stationary Gaussian process which autocorrelation function is determined solving a minimization problem. The simulation method is illustrated through numerical examples issued from civil engineering. Finally, quadratic-mean and almost-sure convergences are studied.
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Contributor : Bénédicte Puig <>
Submitted on : Friday, October 10, 2003 - 1:02:47 PM
Last modification on : Wednesday, December 9, 2020 - 3:05:25 PM
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  • HAL Id : tel-00003526, version 1


Bénédicte Puig. Modélisation et simulation de processus stochastiques non gaussiens. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2003. Français. ⟨tel-00003526⟩



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