Irregularly observed long-memory Levy-driven moving average processes

Mohamedou Ould Haye; Anne Philippe

Irregularly observed long-memory Levy-driven moving average processes

Statistics Theory 2026-08-01 v1 Probability Methodology

Authors: Mohamedou Ould Haye , Anne Philippe

Abstract

We study long-memory continuous-time moving-average processes driven by a Levy process and observed at random renewal times. The sampling scheme introduces an additional source of randomness through irregular observation times. We establish the asymptotic behaviour of normalized partial sums under both finite- and infinite-mean renewal sampling.

Cite

@article{arxiv.2608.00873,
  title  = {Irregularly observed long-memory Levy-driven moving average processes},
  author = {Mohamedou Ould Haye and Anne Philippe},
  journal= {arXiv preprint arXiv:2608.00873},
  year   = {2026}
}