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Stable limit distributions for strongly mixing sequences

Author

Listed:
  • Denker, Manfred
  • Jakubowski, Adam

Abstract

A necessary and sufficient condition for the weak convergence of partial sums of strongly mixing random sequences towards p-stable distributions is established and applied to recent work of Davis (1983) and Jakubowski and Kobus (1987).

Suggested Citation

  • Denker, Manfred & Jakubowski, Adam, 1989. "Stable limit distributions for strongly mixing sequences," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 477-483, October.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:5:p:477-483
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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. Szewczak, Zbigniew S., 2001. "Relative Stability for Strictly Stationary Sequences," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 235-251, August.
    3. 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.
    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. 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.

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