Inference for continuous-time long memory randomly sampled processes

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.