Joint continuity of the local times of fractional Brownian sheets
Ayache, Antoine ; Wu, Dongsheng ; Xiao, Yimin
Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, p. 727-748 / Harvested from Project Euclid
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Let BH={BH(t), t∈ℝ+N} be an (N, d)-fractional Brownian sheet with index H=(H1, …, HN)∈(0, 1)N defined by BH(t)=(BH1(t), …, BHd(t)) (t∈ℝ+N), where BH1, …, BHd are independent copies of a real-valued fractional Brownian sheet B0H. We prove that if d<∑ℓ=1NHℓ−1, then the local times of BH 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 BH. These results are applied to study analytic and geometric properties of the sample paths of BH.
Publié le : 2008-08-15
Classification:  Fractional Brownian sheet,  Liouville fractional Brownian sheet,  Fractional Brownian motion,  Sectorial local nondeterminism,  Local times,  Joint continuity,  Hölder conditions,  60G15,  60G17 
@article{1217964117,
     author = {Ayache, Antoine and Wu, Dongsheng and Xiao, Yimin},
     title = {Joint continuity of the local times of fractional Brownian sheets},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {44},
     number = {2},
     year = {2008},
     pages = { 727-748},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1217964117}
}

Ayache, Antoine; Wu, Dongsheng; Xiao, Yimin. Joint continuity of the local times of fractional Brownian sheets. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp.  727-748. http://gdmltest.u-ga.fr/item/1217964117/