# Deviation inequalities for separately Lipschitz functionals of composition of random functions

## TL;DR

This paper develops deviation and moment inequalities for separately Lipschitz functions of non-homogeneous Markov chains, broadening the understanding of their probabilistic behavior under certain moment conditions.

## Contribution

It introduces new deviation inequalities for Lipschitz functionals of non-homogeneous Markov chains using martingale techniques, applicable to a wide class of models.

## Key findings

- Established deviation inequalities under moment conditions
- Applied martingale methods to non-homogeneous Markov chains
- Extended results to a broad class of natural examples

## Abstract

We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment conditions on some dominating random variables.