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Minimal conditions in p-stable limit theorems -- II

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  • Jakubowski, Adam

Abstract

A p-stable limit theorem holds for partial sums Sn of a stationary sequence, if Sn/Bn --> g[mu] for some 1/p-regularly varying sequence and some non-denegerate strictly p-stable law [mu]. The case 0

Suggested Citation

  • Jakubowski, Adam, 1997. "Minimal conditions in p-stable limit theorems -- II," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 1-20, May.
    • Handle: RePEc:eee:spapps:v:68:y:1997:i:1:p:1-20
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    References listed on IDEAS

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    1. Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
    2. Denker, Manfred & Jakubowski, Adam, 1989. "Stable limit distributions for strongly mixing sequences," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 477-483, October.
    3. Kobus, M., 1995. "Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 199-244, February.
    4. 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.
    5. Jakubowski, Adam, 1994. "On multidimensional domains of attraction for stationary sequences," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 321-326, March.
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    Cited by:

    1. 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.
    2. 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.
    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.

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