Random discretization of stationary continuous time processes
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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