The Annals of Probability

Discrete-Time Stable Processes and Their Certain Properties

Yuzo Hosoya

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Abstract

In this paper we derive the characteristic functions of multivariate stable distributions; specifically the canonical representation of symmetric stable laws is given. Based on that representation, we construct linear stable processes (which include autoregressive stable processes) and stable processes with spectral representation. A sufficient condition for linear stable processes to be regular is given; the complete regularity of autoregressive stable processes is proved. Furthermore, we derive the asymptotic distribution of the Fourier transform of a sample from stable processes with spectral representation.

Article information

Source
Ann. Probab., Volume 6, Number 1 (1978), 94-105.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995613

Digital Object Identifier
doi:10.1214/aop/1176995613

Mathematical Reviews number (MathSciNet)
MR455098

Zentralblatt MATH identifier
0374.60045

JSTOR
links.jstor.org

Subjects
Primary: 60G05: Foundations of stochastic processes
Secondary: 60G10: Stationary processes

Keywords
Stable process multivariate symmetric stable distributions spectral representation regularity characteristic function Fourier transformation

Citation

Hosoya, Yuzo. Discrete-Time Stable Processes and Their Certain Properties. Ann. Probab. 6 (1978), no. 1, 94--105. doi:10.1214/aop/1176995613. https://projecteuclid.org/euclid.aop/1176995613


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