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.

中文翻译：

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平稳连续时间过程的随机离散化

本文研究了随机采样后平稳连续时间过程的二阶性质。虽然短记忆过程总是会产生短记忆过程，但我们证明，当采样定律有很重的尾巴时，长记忆会消失。尽管过程的正态性不是通过随机采样保持的，但归一化的部分求和过程收敛到分数布朗运动，至少在保留长记忆参数时是这样。