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February, 1978 Discrete-Time Stable Processes and Their Certain Properties
Yuzo Hosoya
Ann. Probab. 6(1): 94-105 (February, 1978). DOI: 10.1214/aop/1176995613


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.


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Yuzo Hosoya. "Discrete-Time Stable Processes and Their Certain Properties." Ann. Probab. 6 (1) 94 - 105, February, 1978.


Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60045
MathSciNet: MR455098
Digital Object Identifier: 10.1214/aop/1176995613

Primary: 60G05
Secondary: 60G10

Keywords: Characteristic function , Fourier transformation , multivariate symmetric stable distributions , regularity , ‎spectral representation , Stable process

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
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