R上对称Cauchy过程像集的确切Hausdorff测度  

The Exact Hausdorff Measure for the Range of a Symmetric Cauchy Process in R

作　　者：梁龙跃 石海华 LIANG Longyue;SHI Haihua(School of Economics,Guizhou University,Guiyang,550025,China;College of Science,Nanjing University of Science and Technology,Nanjing,211194,China)

机构地区：[1]贵州大学经济学院,贵阳550025 [2]南京理工大学理学院,南京211194

出　　处：《应用概率统计》2020年第1期11-25,共15页Chinese Journal of Applied Probability and Statistics

基　　金：2017年贵州大学贵州省农林经济管理国内一流学科建设项目(编号:GNYL[2017]002);贵州大学引进人才科研项目(批准号:2015002)资助。

摘　　要：本文通过R上对称Cauchy过程轨道的占时测度与其游离次数的渐近等价关系,建立了过程占时测度的上极限型重对数律.进一步,利用密度定理及经济的轨道覆盖方法得到R上对称Cauchy过程像集的确切Hausdorff测度.This paper establishes limsup type law of the iterated logarithm of the occupation measure,using the asymptotic equivalence relation between the occupation measure and the number of excursion process of a symmetric Cauchy process.Furthermore,by using the density theorem and the economic coverage method,it derives the exact Hausdorff measure for the range of a symmetric Cauchy process in R.

关 键 词：对称Cauchy过程 占时测度 重对数律 HAUSDORFF测度 

分 类 号：O211.6[理学—概率论与数理统计]