布朗单的矩形增量快点集Hausdorff维数

The Hausdorff Dimension of Fast Points Determinded by Rectangle Increments of Brownian Sheet

主要讨论布朗单样本轨道的重分形分析特征,获得布朗单W={W(s):s∈R+N}样本轨道关于矩形增量的“快点集”的Hausdorff维数结果:对任意T>0,0≤α≤1。

In this paper, the multifractal analysis about sample paths of Brownian sheet W={W（s）：s∈R＋^N} is discussed. The Hansdorff dimension results of fast points determinded by rectangle increments of Brownian sheet is obtained, and it is shown that for any T〉0 and 1≥α≥0,dim{s∈（0,T]^N：lim sup h=（h1,h2）↓0｜W｜（（s,s＋h]）｜/√2｜（s,s＋h]｜log1/｜（s,s＋h]｜≥α}=N（1-α^2）