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Random discretization of stationary continuous time processes

Author

Listed:
  • Anne Philippe

    (Université de Nantes)

  • Caroline Robet

    (Université de Nantes)

  • Marie-Claude Viano

    (Université de Lille 1)

Abstract

This paper investigates second order properties of a stationary continuous time process after random sampling. While a short memory process always gives rise to a short memory one, we prove that long-memory can disappear when the sampling law has very heavy tails. Despite the fact that the normality of the process is not maintained by random sampling, the normalized partial sum process converges to the fractional Brownian motion, at least when the long memory parameter is preserved.

Suggested Citation

  • Anne Philippe & Caroline Robet & Marie-Claude Viano, 2021. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 375-400, April.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:3:d:10.1007_s00184-020-00783-1
    DOI: 10.1007/s00184-020-00783-1
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    References listed on IDEAS

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    Cited by:

    1. Mohamedou Ould Haye & Anne Philippe & Caroline Robet, 2024. "Inference for continuous-time long memory randomly sampled processes," Statistical Papers, Springer, vol. 65(5), pages 3111-3134, July.

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