Analyse spectrale Dans les champs aleatoires Non lineaires

Abstract

This thesis is devoted mainly to the study of spectral analysis of random fields, which based on the Fourier analysis and wavelet analysis. Among the numerous random fields in the literature, we have chosen to explore a particular class of models which are capable of taking into account the non Gaussianity character and spatiality behavior. Principally we study the L₂- structure of some SBL models and we establish the spectral density estimation, then we obtained the bispectral and higher order spectral density estimation in which these results can be used to discriminate between linear and nonlinear models. We show also that the estimator of the parameter obtained as minimum of a particular quadratic form which depends on the second and third spectra is consistent and asymptotically normal under certain assumptions. However, In the second part of this thesis, we are interested to examine the fundamental concepts needed in the study of the wavelet transform and random fields. Finally, we consider the nonlinear wavelet estimators of the spectral density and we continued investing in estimation by proposing wavelet-thresholding estimator of the bispectrum.