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Minimal conditions in p-stable limit theorems

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  • Jakubowski, Adam

Abstract

Let be a stationary sequence of random variables with partial sums Sn. Necessary and sufficient conditions are found for weak convergence , where [mu] is strictly p-stable and Bn --> [infinity] is 1/p-regularly varying. Limit theorems involving centering are also discussed.

Suggested Citation

  • Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
    • Handle: RePEc:eee:spapps:v:44:y:1993:i:2:p:291-327
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    Cited by:

    1. Zbigniew S. Szewczak, 2009. "On Limit Theorems for Continued Fractions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 239-255, March.
    2. Szewczak, Zbigniew S., 2016. "Convergence of moments for strictly stationary sequences," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 200-203.
    3. Szewczak, Zbigniew S., 2001. "Relative Stability for Strictly Stationary Sequences," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 235-251, August.
    4. Peligrad, Magda & Utev, Sergey, 2006. "Another approach to Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 279-292, February.
    5. 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.
    6. Bennedsen, Mikkel & Lunde, Asger & Shephard, Neil & Veraart, Almut E.D., 2023. "Inference and forecasting for continuous-time integer-valued trawl processes," Journal of Econometrics, Elsevier, vol. 236(2).
    7. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    8. 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.
    9. Jakubowski, Adam, 1997. "Minimal conditions in p-stable limit theorems -- II," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 1-20, May.
    10. Yannick Malevergne & Pedro Santa-Clara & Didier Sornette, 2009. "Professor Zipf goes to Wall Street," NBER Working Papers 15295, National Bureau of Economic Research, Inc.
    11. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.

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