Dimensional Properties of Fractional Brownian Motion  

作　　者：Dong Sheng WU Yi Min XIAO 

机构地区：[1]Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48824, USA

出　　处：《Acta Mathematica Sinica,English Series》2007年第4期613-622,共10页数学学报（英文版）

基　　金：Research partially supported by NSF Grant DMS-0404729

摘　　要：Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.

关 键 词：fractional Brownian motion Hausdorff dimension uniform dimension results strong local nondeterminism 

分 类 号：O211[理学—概率论与数理统计]