## Nagoya Mathematical Journal

### Two-dimensional symmetric stable distributions and their projections

Katsuya Kojo

#### Abstract

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

#### Article information

Source
Nagoya Math. J., Volume 180 (2005), 135-149.

Dates
First available in Project Euclid: 14 December 2005

https://projecteuclid.org/euclid.nmj/1134569900

Mathematical Reviews number (MathSciNet)
MR2186673

Zentralblatt MATH identifier
1087.60016

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions

#### Citation

Kojo, Katsuya. Two-dimensional symmetric stable distributions and their projections. Nagoya Math. J. 180 (2005), 135--149. https://projecteuclid.org/euclid.nmj/1134569900

#### References

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