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[alpha]-Stable limit theorems for sums of dependent random vectors

Author

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  • Jakubowski, Adam
  • Kobus, Maria

Abstract

Several [alpha]-stable limit theorems for sums of dependent random vectors are proved via point processes theory; p-mixing, m-dependence, and the type of mixing treated within the extreme value theory are considered.

Suggested Citation

  • Jakubowski, Adam & Kobus, Maria, 1989. "[alpha]-Stable limit theorems for sums of dependent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 219-251, May.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:2:p:219-251
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    Citations

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    Cited by:

    1. Bojan Basrak & Danijel Krizmanić, 2015. "A Multivariate Functional Limit Theorem in Weak $$M_{1}$$ M 1 Topology," Journal of Theoretical Probability, Springer, vol. 28(1), pages 119-136, March.
    2. Tyran-Kaminska, Marta, 2010. "Convergence to Lévy stable processes under some weak dependence conditions," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1629-1650, August.
    3. Damarackas, Julius & Paulauskas, Vygantas, 2017. "Spectral covariance and limit theorems for random fields with infinite variance," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 156-175.
    4. Jakubowski, Adam, 1997. "Minimal conditions in p-stable limit theorems -- II," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 1-20, May.
    5. Marcin Pitera & Aleksei Chechkin & Agnieszka Wyłomańska, 2022. "Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 387-424, June.
    6. El Machkouri, Mohamed & Jakubowski, Adam & Volný, Dalibor, 2020. "Stable limits for Markov chains via the Principle of Conditioning," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1853-1878.
    7. Raluca M. Balan & Sana Louhichi, 2009. "Convergence of Point Processes with Weakly Dependent Points," Journal of Theoretical Probability, Springer, vol. 22(4), pages 955-982, December.

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