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Properties of certain symmetric stable distributions

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  • Miller, Grady

Abstract

Necessary and sufficient conditions are presented for jointly symmetric stable random vectors to be independent and for a regression involving symmetric stable random variables to be linear. The notion of n-fold dependence is introduced for symmetric stable random variables, and under this condition we determine all monomials in such random variables for which moments exist.

Suggested Citation

  • Miller, Grady, 1978. "Properties of certain symmetric stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 346-360, September.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:3:p:346-360
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    Cited by:

    1. Rutkowski, Marek, 1995. "Left and right linear innovations for a multivariate S[alpha]S random variable," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 175-184, February.
    2. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    3. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    4. Molchanov, Ilya, 2009. "Convex and star-shaped sets associated with multivariate stable distributions, I: Moments and densities," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2195-2213, November.
    5. Kowalski, Aleksander & Rudiuk, Edmund, 2005. "Correlation in Lp-spaces," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 20-29, September.
    6. Li, Hui & Wu, Min & Wang, Xiao-Tian, 2009. "Fractional-moment Capital Asset Pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 412-421.

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