稳定随机游动二重时集的离散Hausdorff维数

Discrete Hausdorff Dimension of The Double time Set of Intersection of Stable Random Walk

设{Xn}n>0是d维格子点上相应于正则变差函数b（n)=n^(1/8)S_(n)则的稳定随机游动,称 A_B^d={(n,m)∈Z^2 ,Xn=Xm,n<m} 为{Xn}m>0的二重时集,本文讨论了A_β~d的离散Hausdorff维数,并且在较弱的条件下证明了:dim_H(A_β~d)=^(a.s){当d>β时 1\当d≤时 2-d/β}

Let {Xn}n>0 be a stable random work which is relative to the function of regularvariation b(n) =n1/bS(n), andis its Double time set of intersection. In this paper, the discrete Hausdorff dimension problem for Aa is investigated. Ae a result, it is proved that