A Generalized Convolution Model and Estimation for Non-Stationary Random Functions Francky Fouedjio, Nicolas Desassis, Jacques Rivoirard
A Generalized Convolution Model and Estimation for Non-stationary Random Functions Francky Fouedjio, Nicolas Desassis, Jacques Rivoirard To cite this version: Francky Fouedjio, Nicolas Desassis, Jacques Rivoirard. A Generalized Convolution Model and Esti- mation for Non-stationary Random Functions. 2014. hal-01090354 HAL Id: hal-01090354 https://hal-mines-paristech.archives-ouvertes.fr/hal-01090354 Preprint submitted on 3 Dec 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A Generalized Convolution Model and Estimation for Non-stationary Random Functions F. Fouedjio, N. Desassis, J. Rivoirard Equipe´ G´eostatistique- Centre de G´eosciences,MINES ParisTech 35, rue Saint-Honor´e,77305 Fontainebleau, France Abstract Standard geostatistical models assume second order stationarity of the underlying Random Function. In some in- stances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this paper, we introduce a new model for second order non-stationary Random Functions as a convo- lution of an orthogonal random measure with a spatially varying random weighting function. This new model is a generalization of the common convolution model where a non-random weighting function is used.
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