# $\beta$-mixing and moments properties of a non-stationary copula-based Markov process

## TL;DR

This paper establishes conditions for a non-stationary copula-based Markov process to be $eta$-mixing and introduces a convolution-based Gaussian Markov process that generalizes random walks with dependent increments.

## Contribution

It provides new conditions for $eta$-mixing in non-stationary copula-based Markov processes and introduces a generalized Gaussian Markov process with dependent increments.

## Key findings

- Conditions for $eta$-mixing are derived.
- A new convolution-based Gaussian Markov process is introduced.
- The process generalizes standard random walks with dependent increments.

## Abstract

This paper provides conditions under which a non-stationary copula-based Markov process is $\beta$-mixing. We introduce, as a particular case, a convolution-based gaussian Markov process which generalizes the standard random walk allowing the increments to be dependent.