The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process  

作　　者：Shui Cao ZHENG Huo Nan LIN Di He HU 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2005年第5期1137-1148,共12页数学学报（英文版）

基　　金：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.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：Stable process Level sets Local time Hausdorit measure 

分 类 号：O175.21[理学—数学]