A Note on Physical Dependence and Mixing Conditions for Triangular Arrays
Probability
2026-02-05 v1 Statistics Theory
Statistics Theory
Abstract
Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the -mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical dependence implies -mixing and strong mixing for triangular arrays, complementing Hill (2025), who proved the converse implication under moment assumptions.
Cite
@article{arxiv.2602.04250,
title = {A Note on Physical Dependence and Mixing Conditions for Triangular Arrays},
author = {Florian Heinrichs},
journal= {arXiv preprint arXiv:2602.04250},
year = {2026}
}
Comments
Keywords: Weak Dependence, Strong Mixing, $\beta$-Mixing, Physical Dependence, Triangular Arrays, Local Stationarity