稳定分量过程象集的一致测度和一致维数  

Uniform Measure and Uniform Dimension Results for the Image of Subset under Processes with Stable Components

作　　者：赵兴球[1] 

机构地区：[1]武汉大学,武汉430072

出　　处：《应用概率统计》1995年第3期283-288,共6页Chinese Journal of Applied Probability and Statistics

摘　　要：令X(t)=(X_1(t),…,X_N(t))为一d-维过程,其中X_i(t)为α_i-阶d_i-维稳定过程.设0<α_n<…<α_1≤2,d=d_1+…+d_N.本文中,我们获得了,当α_1≤d_1时稳定分量过程X(t)关于Borel集E的象X(E)的Hausdorff测度和Packing测度的一致上界和一致下界,当α_1>d_1时得到了相应测度的一个一致上界.同时我们给出了一致维数结果.Let X(t) = (X_1(t), …, X_n(t)) be a d-dimensional process, where X_i(t) is a α_i,-order stable d_i-dimensional process. Assume 0 < α_N < …<α_1≤ 2, d = d_1 +…+d_N. In this paper, when α_1 ≤ d_1, we obtain the uniform bounds on the Hausdorff and packing measure of the image X(E) of a Borel set E under a process X(t) with stable components. When α_1 > d_1, the uniform upper is obtained. Uniform dimension theorem is given.

关 键 词：稳定分量过程 稳定过程 象集 测度 维数 

分 类 号：O211.62[理学—概率论与数理统计]