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A bivariate stable characterization and domains of attraction

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  • Resnick, Sidney
  • Greenwood, Priscilla
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    Abstract

    Bivariate stable distributions are defined as those having a domain of attraction, where vectors are used for normalization. These distributions are identified and their domains of attraction are given in a number of equivalent forms. In one case, marginal convergence implies joint convergence. A bivariate optional stopping property is given. Applications to bivariate random walk are suggested.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 9 (1979)
    Issue (Month): 2 (June)
    Pages: 206-221

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    Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:206-221

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    Related research

    Keywords: Stable distributions domain of attraction bivariate distributions;

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    Cited by:
    1. Giuseppe Cavaliere & Iliyan Georgiev, 2013. "Exploiting infinite variance through Dummy Variables in non-stationary autoregressions," Quaderni di Dipartimento 1, Department of Statistics, University of Bologna.
    2. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    3. Peter C.B. Phillips, 1993. "Robust Nonstationary Regression," Cowles Foundation Discussion Papers 1064, Cowles Foundation for Research in Economics, Yale University.
    4. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    5. Wu, Chufang, 1997. "New characterization of Marshall-Olkin-type distributions via bivariate random summation scheme," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 171-178, June.
    6. Kozubowski, Tomasz J. & Meerschaert, Mark M. & Panorska, Anna K. & Scheffler, Hans-Peter, 2005. "Operator geometric stable laws," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 298-323, February.

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