摘要
本文研究Sierpinski Gasket上的布朗运动X的象集、图集的Hausdorff维数性质,证明了存在零概率集Ⅳ,若ω∈Nc,则对任意紧集F(?)[0,∞),有(i)dimX(F+t)=min(α-1dimF,df),a.e.t>0,(ii)dimGrX|F+t=min(α-1dimF,(1-α)df+dimF),a.e.t>0,其中ds=log3/log2,α=log2/log5.
In this paper, the Hausdorff dimension of Brownian Motion X on the Sierpinski Gasket is discussed, and it is proved that, there exists a single set N with probability zero, and the following statements are true outside N
(i) For each closed F C [0,1]
dimX(F + t) = min(a-1dimF, df), a.e. t > 0, (ii) For each closed F C [0,1]
dimGrX|F+t= min(a-1dimF, (1 - a)df + dimF), a.e. t > 0, where df = log3/log2,a=log2/log5.
出处
《系统科学与数学》
CSCD
北大核心
2003年第4期542-549,共8页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金资助课题(19871006)
关键词
布朗运动
维数性质
证明
概率性质
函数
Brownian Motion, Hausdorff dimension, Sierpinski Gasket.
