梁龙跃, 石海华. \mathbb{R}上对称Cauchy过程像集的确切Hausdorff测度[J]. 应用概率统计, 2020, 36(1): 11-25. DOI: 10.3969/j.issn.1001-4268.2020.01.002
引用本文: 梁龙跃, 石海华. \mathbb{R}上对称Cauchy过程像集的确切Hausdorff测度[J]. 应用概率统计, 2020, 36(1): 11-25. DOI: 10.3969/j.issn.1001-4268.2020.01.002
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LIANG Longyue, SHI Haihua. The Exact Hausdorff Measure for the Range of a Symmetric Cauchy Process in \mathbb{R}[J]. Chinese Journal of Applied Probability and Statistics, 2020, 36(1): 11-25. DOI: 10.3969/j.issn.1001-4268.2020.01.002
Citation: LIANG Longyue, SHI Haihua. The Exact Hausdorff Measure for the Range of a Symmetric Cauchy Process in \mathbb{R}[J]. Chinese Journal of Applied Probability and Statistics, 2020, 36(1): 11-25. DOI: 10.3969/j.issn.1001-4268.2020.01.002
shu

\mathbbR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 \mathbbR

    摘要
  • 摘要: 本文通过\mathbbR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\mathbbR上对称Cauchy过程像集的确切Hausdorff测度.

     

    Abstract: 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 \mathbbR.

     

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