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Two-dimensional symmetric stable distributions and Their projections

Published online by Cambridge University Press:  11 January 2016

Katsuya Kojo
Katsuya Kojo*
Affiliation:
Niihama National College of Technology Niihama, 792-8580Japankojo@sci.niihama-nct.ac.jp
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Abstract

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We study the problem whether a given 2-dimensional symmetric stable distribution with index α (0 < α ≤ 1) is determined by its 1-dimensional projections in some specified directions. We give some conditions for the affirmative answer and for the negative answer.

Keywords

60E07
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 180 , 2005 , pp. 135 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[1] Marcus, D. J., Non-stable laws with all projections stable, Z. Wahrsch. verw. Gebiete, 64 (1983), 139–156.Google Scholar
[2] Samorodnitsky, G. and Taqqu, M. S., Stable non-Gaussian random processes, Chapman & Hall, New York, 1994.Google Scholar