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

Let X_nn≥0 be a stable random work which is relative to the function of regularvariation b（n）=n^1/βS(n), and A_\beta^d=\left\(n, m) \in Z_<:^2 X_n=X_n n, nA _β^α is investigated. Ae a result, it is proved that \operatornamedim_H\left(A_β^\alpha\right) \stackrela . s=\left\\beginarrayl1 \quad \text 当 d>\beta \text 时 \\ 2-\fracd\beta \quad \text 当 d \leqslant \beta \text 时 \endarray\right..