Some Results on Fractional Brownian Sheets and Their Local Times  

作　　者：Zong-mao Chen Zheng-yan Lin 

机构地区：[1]Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University, Hangzhou310018, China [2]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第4期669-676,共8页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10571159);Specialized Research Found for Doctor Program of Higher Education(No.20060335032);Hangdian Foundation(No.KYS091506042).

摘　　要：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].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].

关 键 词：Fractional Brownian sheet local time Hausdorff measure 

分 类 号：O1[理学—数学]