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Some mixing conditions for stationary symmetric stable stochastic processes

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  • Gross, Aaron

Abstract

We derive some necessary and sufficient conditions for mixing of non-Gaussian stationary symmetric stable processes in terms of the spectral representation, and derive additional conditions for the special case where the spectral representation itself is stationary. We also define equivalence relations on symmetric stable processes, and then show that the mixing property respects the equivalence relations.

Suggested Citation

  • Gross, Aaron, 1994. "Some mixing conditions for stationary symmetric stable stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 51(2), pages 277-295, July.
    • Handle: RePEc:eee:spapps:v:51:y:1994:i:2:p:277-295
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    Cited by:

    1. Magdziarz, Marcin, 2009. "Correlation cascades, ergodic properties and long memory of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3416-3434, October.
    2. Rosinski, Jan & Zak, Tomasz, 1996. "Simple conditions for mixing of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 277-288, February.
    3. Paul Jung, 2014. "Random-Time Isotropic Fractional Stable Fields," Journal of Theoretical Probability, Springer, vol. 27(2), pages 618-633, June.
    4. Riccardo Passeggeri & Almut E. D. Veraart, 2019. "Mixing Properties of Multivariate Infinitely Divisible Random Fields," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1845-1879, December.
    5. Kabluchko, Zakhar & Schlather, Martin, 2010. "Ergodic properties of max-infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 281-295, March.

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