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Pré-Publication, Document De Travail Année : 2019

Random discretization of stationary continuous time processes

Anne Philippe
Caroline Robet
Marie-Claude Viano
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Résumé

This paper investigates the second order properties of a stationary continuous time process after random sampling. While a short memory process gives always 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 perserved.
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Dates et versions

hal-01944290 , version 1 (04-12-2018)
hal-01944290 , version 2 (04-09-2019)

Identifiants

  • HAL Id : hal-01944290 , version 2

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Anne Philippe, Caroline Robet, Marie-Claude Viano. Random discretization of stationary continuous time processes. 2019. ⟨hal-01944290v2⟩
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