Hausdorff Dimension for Range and Graph of Multi-Parameter Operator Stable L\'{e}vy Processes

doi:10.3969/j.issn.1001-4268.2019.06.001

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Abstract

The lower Hausdorff dimension results for the range and the graph of multi-parameter operator stable L\'{e}vy processes are established. The consequences are completely determined by the eigenvalues of its exponent matrix.

Key words�� multi-parameter operator stable L\'{e}vy processes Hausdorff dimension range set graph set

PACS:

O211.61

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The project was supported by the National Natural Science Foundation of China (Grant No. 11601083), the Program for Probability and Statistics: Theory and Application (Grant No. IRTL1704) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ).

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	CHEN Xiaoping
	LIN Huonan

Cite this article:

CHEN Xiaoping,LIN Huonan. Hausdorff Dimension for Range and Graph of Multi-Parameter Operator Stable L\'{e}vy Processes[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2019, 35(6): 551-557.

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http://aps.ecnu.edu.cn/EN/10.3969/j.issn.1001-4268.2019.06.001 OR http://aps.ecnu.edu.cn/EN/Y2019/V35/I6/551