Some results on fractional Brownian sheets and their local times

Abstract

Let B 0 = {B 0 (t), t ∈ R + } be a real-valued fractional Brownian sheet. Define the (N, d)-Gaussian random field B H by B H (t) = (B 1 (t), ..., B (t)) t ∈ R + , where B 1 , ..., B are independent copies of B 0 . The existence and joint continuity of local times of B H is proven in some given conditions in [22]. We then study further properties of the local times of B H , such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].