Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T16:13:50.210Z Has data issue: false hasContentIssue false
  • English
  • Français

A new representation for the characteristic function of strictly geo-stable vectors

Part of: Mathematical economics Stochastic analysis Limit theorems

Published online by Cambridge University Press:  14 July 2016

Lev B. Klebanov ,
Stefan Mittnik ,
Svetlozar T. Rachev  and
Vladimir E. Volkovich
Lev B. Klebanov*
Affiliation:
St Petersburg State University
Stefan Mittnik*
Affiliation:
University of Kiel
Svetlozar T. Rachev*
Affiliation:
University of California, Santa Barbara
Vladimir E. Volkovich*
Affiliation:
Ort Braude College
*
∗ Postal address: St Petersburg State University for Architecture and Civil Engineering, St Petersburg, Russia.
∗∗ Postal address: Institute of Statistics and Econometrics, University of Kiel, Germany.
∗∗∗ Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA. Email address: [email protected]
∗∗∗∗ Postal address: Ort Braude College, PO Box 78, Karmiel 21982, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

A new representation for the characteristic function of the multivariate strictly geo-stable distribution is presented. The representation is appealing from a parametric viewpoint: its parameters have an intuitive probabilistic interpretation; and it is particularly useful for estimating the parameters of the geo-stable distribution.

Keywords

Stable vectorsgeo-stable laws

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60H05: Stochastic integrals 91B84: Economic time series analysis
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1137 - 1142
Copyright
Copyright © by the Applied Probability Trust 2000 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Klebanov, L. B., Maniya, G. M., and Melamed, J. A. (1984). A problem of Zolotarev and analogues of infinitely divisible and stable distributions in a scheme of summing a random number of random variables. Theory Prob. Appl. 29, 791–794.CrossRefGoogle Scholar
[2] Klebanov, L. B., Melamed, J. A., Mittnik, S., and Rachev, S. T. (1996). Integral and asymptotic representations of geo-stable densities. Appl. Math. Lett. 9, 37–40.CrossRefGoogle Scholar
[3] Lisitsky, A. D. (1990). New expression for characteristic function of multidimensional strict stable law. In Problems of Stability for Stochastic Models. VNIISI, Moscow, pp. 49–53 (in Russian).Google Scholar
[4] Mittnik, S., and Rachev, S. T. (1993). Modeling asset returns with alternative stable models. Econ. Rev. 12, 261–330.CrossRefGoogle Scholar
[5] Mittnik, S., and Rachev, S. T. (1993). Reply to comments on ‘Modeling asset returns with alternative stable models’. Econ. Rev. 12, 347–389.CrossRefGoogle Scholar
[6] Rao, C. R. (1973). Linear Statistical Inference and its Applications. John Wiley, New York.CrossRefGoogle Scholar
[7] Samorodnitsky, G., and Taqqu, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, New York.Google Scholar
[8] Zolotarev, V. M. (1983). One-Dimensional Stable Distributions. Nauka, Moscow (in Russian).Google Scholar