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The Exact Hausdorff Measure for the Range of a Symmetric Cauchy Process in \mathbb{R} |
LIANG Longyue; SHI Haihua |
School of Economics, Guizhou University, Guiyang, 550025, China; College of Science, Nanjing University of Science and Technology, Nanjing, 211194, China |
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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 \mathbb{R}.
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