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Stable limits for Markov chains via the Principle of Conditioning

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  • El Machkouri, Mohamed
  • Jakubowski, Adam
  • Volný, Dalibor

Abstract

We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:1853-1878
    DOI: 10.1016/j.spa.2019.06.002
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    References listed on IDEAS

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    1. Denker, Manfred & Jakubowski, Adam, 1989. "Stable limit distributions for strongly mixing sequences," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 477-483, October.
    2. 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.
    3. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
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