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V. Champ-aléatoire-généralisé and . Riemannienne, En particulier, le phénomène en question est décrit par un champ aléatoire (généralement gaussien) et les données observées sont considérées comme résultant d'une réalisation particulière de ce champ aléatoire. Afin de faciliter la modélisation et les traitements géostatistiques qui en découlent, il est d'usage de supposer ce champ comme stationnaire et donc de supposer que la structuration spatiale des données se

, En effet, comment définir cette notion de stationnarité lorsque les données sont indexées sur des domaines non euclidiens (comme des sphères ou autres surfaces lisses)? Quid également du cas où les données présentent structuration spatiale qui change manifestement d'un endroit à l'autre du domaine d'étude? En outre, opter pour des modèles plus complexes, lorsque cela est possible, s'accompagne en général d'une augmentation drastique des coûts opérationnels (calcul et mémoire), Cependant, lorsqu'on travaille avec des jeux de données spatialisées complexes, cette hypothèse devient inadaptée

. Dans, nous proposons une solution à ces problèmes s'appuyant sur la définition de champs aléatoires généralisés sur des variétés riemanniennes. D'une part, travailler avec des champs aléatoires généralisés permet d'étendre naturellement des travaux récents s'attachant à tirer parti d'une caractérisation des champs aléatoires utilisés en géostatistique comme des solutions d'équations aux dérivées partielles stochastiques. D'autre part, travailler sur des variétés riemanniennes permet à la fois de définir des champs sur des domaines qui ne sont que localement euclidiens, et sur des domaines vus comme déformés localement

, Ces champs généralisés sont ensuite discrétisés en utilisant une approche par éléments finis, et nous en donnons une formule analytique pour une large classe de champs généralisés englobant les champs généralement utilisés dans les applications. Enfin, afin de résoudre le problème du passage à l'échelle pour les grands jeux de données, nous proposons des algorithmes inspirés du traitement du signal sur graphe permettant la simulation