Covariation inequality in Grand Lebesgue Spaces

TL;DR

This paper provides an exact estimate for the covariation between two random variables using mixing coefficients, linking it to the fundamental function of rearrangement invariant spaces, advancing understanding in probabilistic inequalities.

Contribution

It introduces a precise covariation estimate in Grand Lebesgue Spaces, connecting it with fundamental functions of rearrangement invariant spaces, which is a novel theoretical development.

Findings

Exact covariation estimate derived for random variables with mixing conditions

Link established between covariation bounds and fundamental functions of rearrangement invariant spaces

Provides a theoretical framework for analyzing dependence in probabilistic spaces

Abstract

We represent in this preprint the exact estimate for covariation berween two random variables (r.v.), which are measurable relative the corresponding sigma-algebras through anyhow mixing coefficients. We associate a solution of this problem with fundamental function for correspondent rearrangement invariant spaces.