Some Results on Fractional Brownian Sheets and Their Local Times

Let B0^H = {B0^H（t）,t ∈ R＋^N） be a real-valued fractional Brownian sheet. Define the （N,d）- Gaussian random field B^H by
B^H（t） = （B1^H（t）,...,Bd^H（t）） t ∈ R＋^N, where B1^H, ..., Bd^H are independent copies of B0^H. 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].

Some results on fractional Brownian sheets and their local times

Let B ₀ ^H = {B ₀ ^H (t), t ∈ R ₊ ^N } be a real-valued fractional Brownian sheet. Define the (N, d)-Gaussian random field B ^H by B ^H (t) = (B ₁ ^H (t), ..., B _d ^H (t)) t ∈ R ₊ ^N , where B ₁ ^H , ..., B _d ^H are independent copies of B ₀ ^H . 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]. Supported by the National Natural Science Foundation of China (No. 10571159), Specialized Research Found for Doctor Program of Higher Education (No. 20060335032) and Hangdian Foundation (No. KYS091506042).