# Estimating the Mixing Coefficients of Geometrically Ergodic Markov Processes

arXiv: https://arxiv.org/abs/2402.07296 · HTML: https://mlsanity.com/paper/2402.07296/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 11 Feb 2024.

## Builds on (most cited first, 2 of 2)

- [Mixing time estimation in reversible Markov chains from a single sample path](https://mlsanity.com/paper/1708.07367/) (2017)
- [Estimating the Mixing Time of Ergodic Markov Chains](https://mlsanity.com/paper/1902.01224/) (2019)

## Built on by (most cited first, 3 of 3)

- [Empirical PAC-Bayes Bounds for Markov Chains](https://mlsanity.com/paper/2509.20985/) (2025)
- [Restless Linear Bandits](https://mlsanity.com/paper/2405.10817/) (2024)
- [Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds](https://mlsanity.com/paper/2610.20007/) (2026)

## Abstract (arXiv)

We propose methods to estimate the individual β-mixing coefficients of a real-valued geometrically ergodic Markov process from a single sample-path X0,X1, dots,Xn. Under standard smoothness conditions on the densities, namely, that the joint density of the pair (X0,Xm) for each m lies in a Besov space Bs1,∞(mathbb R2) for some known s>0, we obtain a rate of convergence of order O(log(n) n-[s]/(2[s]+2)) for the expected error of our estimator in this casefootnoteWe use [s] to denote the integer part of the decomposition s=[s]+s of s ∈ (0,∞) into an integer term and a em strictly positive remainder term s ∈ (0,1].. We complement this result with a high-probability bound on the estimation error, and further obtain analogues of these bounds in the case where the state-space is finite. Naturally no density assumptions are required in this setting; the expected error rate is shown to be of order mathcal O(log(n) n-1/2).