On the identification of hidden pointwise Hölder exponents
نویسندگان
چکیده
Un court résumé en français Mots clés: Processus, Statistique mathématique. L’exposant de Hölder ponctuel (EHP) d’un processus stochastique X permet de mesurer la régularité locale de X. Nombre d’auteurs se sont déjà intéressés au problème de l’estimation de cet exposant à partir de l’observation d’une trajectoire discrétisée de X (voir par exemple [1, 4, 5, 9]). Cependant, il ne semble pas toujours réaliste de supposer qu’une telle observation est directement accessible mais seulement une version corrompue de celle-ci. Est-il alors possible d’effectuer l’estimation ? A notre connaissance, cette question a été assez peu étudiée dans la littérature et les articles qui l’abordent se placent dans un cadre qui est essentiellement celui de processus Gaussiens à accoissements stationnaires [8, 11]; l’EHP a alors une structure relativement simple puisqu’il reste contant au cours du temps. L’objectif de notre exposé est d’etudier cette question dans un cadre nouveau, celui du mouvement Brownien multifractionnaire; l’EHP de ce processus a généralement une structure assez complexe parce qu’il varie d’un instant à l’autre (voir par [3, 10, 2]).
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