Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-08-11T22:23:06.212Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic dependence of moving average type self-similar stable random Fields*

Published online by Cambridge University Press:  22 January 2016

Piotr S. Kokoszka  and
Murad S. Taqqu
Piotr S. Kokoszka
Affiliation:
Boston University, Department of Mathematics, 111 Cummington Street, Boston, MA 02215-2411, USA, Email: piotr@math.bu.edu
Murad S. Taqqu
Affiliation:
Boston University, Department of Mathematics, 111 Cummington Street, Boston, MA 02215-2411, USA, Email: murad@math.bu.edu
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

As non-Gaussian stable stochastic processes have infinite second moments, one cannot use the covariance function to describe their dependence structure.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 130 , June 1993 , pp. 85 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

Footnotes

*

The first author is on leave from the Hugo Steinhaus Center, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation.

References

[1] Astrauskas, A., Levy, J. B., and Taqqu, M. S., The asymptotic dependence structure of the linear fractional Levy motion, Lietuvos Matematikos Rinkinys (Lithuanian Mathematical Journal), 31 (1) (1991), 1–28.Google Scholar
[2] Kokoszka, P. S. and Taqqu, M. S., New classes of self-similar symmetric stable random fields, to appear in J. Theoretical Prob., 1993.Google Scholar
[3] Kokoszka, P. S. and Taqqu, M. S., Asymptotic dependence of statble self-similar processes of Chentsov type, In Hahn, M. G. Dudley, R. M. and Kuelbs, J., editors, Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference, pages 152–165, Boston, 1992. Birkhäuser.CrossRefGoogle Scholar
[4] Kokoszka, P. S. and Taqqu, M. S., Infinite variance stable ARMA processes, to appear in Journal for Time Series Analysis, 1993.Google Scholar
[5] Kreyzig, E., Introductory Functional Analysis with Applications, Wiley & Sons, 1989.Google Scholar
[6] Levy, J. and Taqqu, M. S., A characterization of the asymptotic behavior of stationary stable processes, In Samorodnitsky, G. Cambanis, S. and Taqqu, M. S., editors, Stable Processes and Related Topics, volume 25 of Progress in Probability, pages 181–198, Boston, 1991. Birkhäuser.Google Scholar
[7] Samorodnitsky, G. and Taqqu, M. S., (1 /α)-self-similar processes with stationary increments, J. Multivariate Anal. 35 (1990), 308–313.CrossRefGoogle Scholar
[8] Takenaka, S., Integral-geometric construction of self-similar stable processes, Nagoya Math. J., 123 (1991), 1–12.Google Scholar