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

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  • 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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