Random discretization of stationary continuous time processes

被引：0
作者：
Anne Philippe
Caroline Robet
Marie-Claude Viano
机构：
[1] Université de Nantes,Laboratoire de Mathématiques Jean Leray
[2] Université de Lille 1,Laboratoire Paul Painlevé UMR CNRS 8524, UFR de Mathematiques – Bat M2
来源：
Metrika | 2021年 / 84卷
关键词：
Gaussian process; Long memory; Partial sum; Random sampling; Regularly varying covariance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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收藏
页码：375 / 400
页数：25
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