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

摘要: 设X_n_n≥0是d维格子点上相应于正则变差函数b（n）=n^1/βS(n)则的稳定随机游动,称A_\beta^d=\left\(n, m) \in Z_<:^2 X_n=X_n n, nX_n_n≥0的二重时集,本文讨论了A _β^α的离散Hausdorff维数,并且在较弱的条件下证明了:\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..

Abstract: Let X_n_n≥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..