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Growth rates of sample covariances of stationary symmetric [alpha]-stable processes associated with null recurrent Markov chains

Author

Listed:
  • Resnick, Sidney
  • Samorodnitsky, Gennady
  • Xue, Fang

Abstract

A null recurrent Markov chain is associated with a stationary mixing S[alpha]S process. The resulting process exhibits such strong dependence that its sample covariance grows at a surprising rate which is slower than one would expect based on the fatness of the marginal distribution tails. An additional feature of the process is that the sample autocorrelations converge to non-random limits.

Suggested Citation

  • Resnick, Sidney & Samorodnitsky, Gennady & Xue, Fang, 2000. "Growth rates of sample covariances of stationary symmetric [alpha]-stable processes associated with null recurrent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 321-339, February.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:2:p:321-339
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    Citations

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    Cited by:

    1. Chen, Zaoli & Samorodnitsky, Gennady, 2022. "Extremal clustering under moderate long range dependence and moderately heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 86-116.
    2. Takashi Owada, 2016. "Limit Theory for the Sample Autocovariance for Heavy-Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows," Journal of Theoretical Probability, Springer, vol. 29(1), pages 63-95, March.
    3. Resnick, Sidney & Samorodnitsky, Gennady, 2004. "Point processes associated with stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 191-209, December.
    4. Zaoli Chen & Gennady Samorodnitsky, 2020. "Extreme Value Theory for Long-Range-Dependent Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1894-1918, December.

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