布朗单增量“快点”集的Packing维数

Packing Dimension of "Fast Point" Sets for Brownian Sheet

讨论布朗单样本轨道的重分形分析问题,通过构造一个上极限型分形集的方法,得到其不同的增量形式"快点"集的Packing维数结果.当T>0,0≤α<1,ET(α)时,有Dim(ET(α))=N,Dim(FT(α))=N,Dim(GT(α))=N,a.s..当0<α<1时,ET(α),FT(α)和GT(α)的Hausdorff维数与其Packing维数不相等.

The multifractal analysis for the sample paths of Brownian sheet is discussed in the paper.The packing dimensions of ＂fast point＂ sets with different increment forms of Brownian sheet are given by constructing a random fractals of limsup type.If T0,0≤α1,ET（α）,then Dim（ET（α））=N,Dim（FT（α））=N,Dim（GT（α））=N,（a.s.）.The Hausdorff dimensions of ET（α）,FT（α） and GT（α） isn＇t equal to their packing dimensions if 0a1.