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April 1996 Packing and covering indices for a general Lévy process
William E. Pruitt, S. James Taylor
Ann. Probab. 24(2): 971-986 (April 1996). DOI: 10.1214/aop/1039639373

Abstract

There has been substantial interest in the indices $0 \leq \beta'' \leq \beta' \leq \beta \leq 2$, defined by Blumenthal and Getoor, determined by a general Lévy process in $\mathbf{R}^d$. Pruitt defined an index $\gamma$ which determines the covering dimension and Taylor showed that an index $\gamma'$, first considered by Hendricks, determines the packing dimension for the trajectory. In the present paper we prove that $$\frac{\beta}{2} \le \gamma' \le \min(\beta, d),$$ and give examples to show that the whole range is attainable. However, we cannot completely determine the set of values of $(\gamma, \gamma', \beta)$ which can be attained as indices of some Lévy process.

Citation

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William E. Pruitt. S. James Taylor. "Packing and covering indices for a general Lévy process." Ann. Probab. 24 (2) 971 - 986, April 1996. https://doi.org/10.1214/aop/1039639373

Information

Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0862.60063
MathSciNet: MR1404539
Digital Object Identifier: 10.1214/aop/1039639373

Subjects:
Primary: 60J30
Secondary: 28A75

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 2 • April 1996
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