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Decomposability for stable processes

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  • Wang, Yizao
  • Stoev, Stilian A.
  • Roy, Parthanil

Abstract

We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes.

Suggested Citation

  • Wang, Yizao & Stoev, Stilian A. & Roy, Parthanil, 2012. "Decomposability for stable processes," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1093-1109.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:1093-1109
    DOI: 10.1016/j.spa.2011.11.007
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    References listed on IDEAS

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    1. Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
    2. Pipiras, Vladas, 2007. "Nonminimal sets, their projections and integral representations of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1285-1302, September.
    3. Cambanis, Stamatis & Maejima, Makoto & Samorodnitsky, Gennady, 1992. "Characterization of linear and harmonizable fractional stable motions," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 91-110, August.
    4. Cambanis, Stamatis & Hardin, Clyde D. & Weron, Aleksander, 1987. "Ergodic properties of stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 1-18, February.
    5. Wang, Yizao & Stoev, Stilian A., 2010. "On the association of sum- and max-stable processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 480-488, March.
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