Joint continuity of the local times of fractional Brownian sheets

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dc.creatorAyache, Antoine
dc.creatorWu, Dongsheng
dc.creatorXiao, Yimin
dc.date2008-08-22
dc.date.accessioned2026-07-07T09:57:56Z
dc.date.available2026-07-07T09:57:56Z
dc.descriptionLet $B^H=\{B^H(t),t\in{\mathbb{R}_+^N}\}$ be an $(N,d)$-fractional Brownian sheet with index $H=(H_1,...,H_N)\in(0,1)^N$ defined by $B^H(t)=(B^H_1(t),...,B^H_d(t)) (t\in {\mathbb{R}}_+^N),$ where $B^H_1,...,B^H_d$ are independent copies of a real-valued fractional Brownian sheet $B_0^H$. We prove that if $d<\sum_{\ell=1}^NH_{\ell}^{-1}$, then the local times of $B^H$ are jointly continuous. This verifies a conjecture of Xiao and Zhang (Probab. Theory Related Fields 124 (2002)). We also establish sharp local and global Hölder conditions for the local times of $B^H$. These results are applied to study analytic and geometric properties of the sample paths of $B^H$.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AIHP131 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0808.3054
dc.identifierhttp://arxiv.org/abs/0808.3054
dc.identifierAnnales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 4, 727-748
dc.identifierdoi:10.1214/07-AIHP131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167532
dc.subjectProbability
dc.titleJoint continuity of the local times of fractional Brownian sheets
dc.typetext

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