# Inference for continuous-time long memory randomly sampled processes

## TL;DR

This paper studies the properties of discretely sampled long memory processes derived from continuous-time Gaussian processes, focusing on their second-order characteristics and asymptotic behavior in time and frequency domains.

## Contribution

It provides new insights into the second-order properties and asymptotic results of randomly sampled long memory processes, especially when the original process is Gaussian.

## Key findings

- Derived asymptotic results in time and frequency domains.
- Characterized second-order properties of sampled processes.
- Analyzed the impact of random sampling on Gaussian processes.

## Abstract

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly focus on the case when the initial process is Gaussian. The challenge being that, although marginally remains Gaussian, the randomly sampled process will no longer be jointly Gaussian.