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Ayache, Antoine; Wu, Dongsheng; Xiao, Yimin
Joint continuity of the local times of fractional brownian sheets. Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, 44 no. 4 (2008), p. 727-748
Texte intégral djvu | pdf | Analyses MR 2446295 | Zbl 1180.60032
Class. Math.: 60G15, 60G17
Mots clés: fractional brownian sheet, Liouville fractional brownian sheet, fractional brownian motion, sectorial local nondeterminism, local times, joint continuity, Hölder conditions

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Résumé

Désignons par BH={BH(t), t∈ℝ+N} le (N, d)-drap Brownien fractionnaire de paramètre H=(H1, …, HN)∈(0, 1)N défini par BH(t)=(BH1(t), …, BHd(t)) (t∈ℝ+N), où BH1, …, BHd sont des copies indépendantes du drap Brownien fractionnaire à valeurs réelles B0H. Nous montrons que le temps local de BH est bicontinu lorsque d<∑=1NH−1. Cela résout une conjecture de Xiao et Zhang (Probab. Theory Related Fields 124 (2002)). Nous obtenons aussi des résultats fins concernant la régularité Hölderienne, locale et globale, du temps local. Ces résultats nous permettent d’étudier certaines propriétés analytiques et géométriques des trajectoires de BH.

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