稳定随机游动水平集的离散豪斯道夫维数

DISCRETE HAUSDORFF DIMEUSION FO THE LEVEL SET OF A STABLE RANDOM WALK

设{X■}是Zd上的正则函数为b（n）=n1/αS（n）的稳定随机游动.Z（a）是过程在a的水平集,本文证明了Z（a）的离散豪斯道夫维数等于1-（d/2）,这个结果与稳定连续过程一致。

Let {X_n}_(n≥0) be a stable random walk which is relative to the regular function b(n) = n^(1/a)s(n) in Z^d,and Z(a)= {n≥0:x_a= a} is its level set at a.In this paper,the discrete Mausdorff dimension problem of Z(a) is investigated.As a result,it is proved that dim_H(Z(a))(?) 1-d/a