The Engel algorithm for absorbing Markov chains

TL;DR

This paper introduces Engel's chip-moving algorithm for analyzing absorbing Markov chains, providing a proof of its correctness, which was previously unpublished, making it suitable for educational purposes.

Contribution

It presents and proves the validity of Engel's algorithm for calculating quantities in absorbing Markov chains, filling a gap in existing literature.

Findings

The algorithm correctly computes basic quantities for absorbing Markov chains.

A proof of the algorithm's correctness is provided.

The method is suitable for introductory probability courses.

Abstract

In this module, suitable for use in an introductory probability course, we present Engel's chip-moving algorithm for finding the basic descriptive quantities for an absorbing Markov chain, and prove that it works. The tricky part of the proof involves showing that the initial distribution of chips recurs. At the time of writing (circa 1979) no published proof of this was available, though Engel had stated that such a proof had been found by L. Scheller.