# Inheritance of strong mixing and weak dependence under renewal sampling

arXiv: https://arxiv.org/abs/2007.00574 · HTML: https://mlsanity.com/paper/2007.00574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Robust deep learning from weakly dependent data](https://mlsanity.com/paper/2405.05081/) (2024)

## Abstract (arXiv)

Let X be a continuous-time strongly mixing or weakly dependent process and T a renewal process independent of X with inter-arrival times τ. We show general conditions under which the sampled process (XTi,Ti-Ti-1)top is strongly mixing or weakly dependent. Moreover, we explicitly compute the strong mixing or weak dependence coefficients of the renewal sampled process and show that exponential or power decay of the coefficients of X is preserved (at least asymptotically). Our results imply that essentially all central limit theorems available in the literature for strongly mixing or weakly dependent processes can be applied when renewal sampled observations of the process X are at disposal.