| The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process |
| |
| 引用本文： | Shui Cao ZHENG Huo Nan LIN Di He HU. The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process[J]. 数学学报(英文版), 2005, 21(5): 1137-1148. DOI: 10.1007/s10114-004-0521-1 |
| |
| 作者姓名： | Shui Cao ZHENG Huo Nan LIN Di He HU |
| |
| 作者单位： | [1]School of Mathematics Sciences, Peking University, Beijing 100871, P. R. China [2]School of Sciences, Jimei University, Xiamen 361021, P. R. China [3]Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China [4]College of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China |
| |
| 基金项目： | Supported partly by the NNSF of China （Nos. 10371092, 10171015 and No. 10271027） |
| |
| 摘 要： | In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.
|
| 关 键 词： | Hausdorff测量函数 稳定过程 水平集 对称性 |
| 收稿时间： | 2003-03-12 |
| 修稿时间： | 2003-03-122003-12-12 |
The Exact Hausdorff Measure Function of the Level Sets of Multi–parameter Symmetric Stable Process |
| |
| Shui Cao Zheng,Huo Nan Lin,Di He Hu. The Exact Hausdorff Measure Function of the Level Sets of Multi–parameter Symmetric Stable Process[J]. Acta Mathematica Sinica(English Series), 2005, 21(5): 1137-1148. DOI: 10.1007/s10114-004-0521-1 |
| |
| Authors: | Shui Cao Zheng Huo Nan Lin Di He Hu |
| |
| Affiliation: | (1) School of Mathematics Sciences, Peking University, Beijing 100871, P. R. China;(2) School of Sciences, Jimei University, Xiamen 361021, P. R. China;(3) Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China;(4) College of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China |
| |
| Abstract: | In this paper, we investigate the Hausdorff measure for level sets of N–parameter R d –valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N–parameter R d –valued stable processes. We show that the exact Hausdorff measure function of level sets of N–parameter R d –valued symmetric stable processes of index α is ϕ(r) = r N−d/α (log log 1/r) d/α when Nα > d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d,α) strictly stable processes. Supported partly by the NNSF of China (Nos. 10371092, 10171015 and No. 10271027) |
| |
| Keywords: | Stable process Level sets Local time Hausdorit measure |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
