# Notes on: Rosenthal, J. S. (1995): Minorization conditions and convergence rates for markov chain monte carlo

## Table of Contents

## Overview

- Provides a method for proving rigorous, a priori bounds on the number of iterations required until satisfactory convergence has taken place

## Notation

- is the MC
**transition kernel**on a**state space**

## Definitions

We say the transition kernel on the state space satisfy a **minorization condition** or **split** on a subsets if there is a probability measure on , a positive integer , and , such that

for all measureable subsets .