Local times of fractional Brownian sheets

Abstract

Let B0H = {B0H (t), t ∈ ℝ+N} be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field BH defined by BH (t) = (B1H (t), ..., BdH (t)) (t ∈ ℝ+N), where B1H, ..., BdH are independent copies of B0H. In this paper, the existence and joint continuity of the local times of BH are established.