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].