Constructing Markov chains with given dependence and marginal stationary distributions

TL;DR

This paper presents a method to construct Markov chains on finite state spaces with specified stationary distributions, dependence structures, and marginal distributions, utilizing information geometry and an algorithmic approach.

Contribution

It introduces a novel construction method for Markov chains based on three key constraints, leveraging the generalized Pythagorean theorem in information geometry.

Findings

Provides an explicit algorithm for constructing the chains

Demonstrates the method with integer-valued autoregressive processes

Bridges information geometry with Markov chain design

Abstract

A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints: stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry plays a central role in the construction. An algorithm for obtaining the desired Markov chain is described. Integer-valued autoregressive processes are considered for illustration.