On A Stein Method Based Approximation for A Two-Dimensional Markov Chain

TL;DR

This paper introduces a Stein method-based approach to approximate the stationary distribution of a two-dimensional Markov chain, involving novel techniques for moment estimation and solving the Poisson equation.

Contribution

It develops innovative methods for estimating moments and solving the Poisson equation to improve stationary distribution approximation of Markov chains.

Findings

Effective moment estimation techniques for 2D Markov chains

New solutions for the Poisson equation with PDEs

Enhanced approximation accuracy for stationary distributions

Abstract

We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the Poisson equation with a partial differential operator.