Joint continuity of the local times of fractional Brownian sheets

Antoine Ayache, Dongsheng Wu, Yimin Xiao

Let $B^H=\{B^H(t),t\in {\mathbb{R}}_{+}^N\}$ 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…