A Comment on the Book "Continuous-Time Markov Chains" by W.J. Anderson

TL;DR

This paper critiques W.J. Anderson's book on continuous-time Markov chains, clarifying misunderstandings about approximating methods to prevent future confusion among researchers.

Contribution

It identifies and corrects errors in Anderson's book regarding approximating methods in continuous-time Markov chains.

Findings

Several results in the book are incorrectly stated or proved.

Clarification of approximating methods for continuous-time Markov chains.

Emphasis on the importance of correct application of approximation techniques.

Abstract

The book "Continuous-Time Markov Chains" by W. J. Anderson collects a large part of the development in the past thirty years. It is now a popular reference for the researchers on this subject or related fields. Unfortunately, due to a misunderstanding of the approximating methods, several results in the book are incorrectly stated or proved. Since the results are related to the present author's work, to whom it may be a duty to correct the mistakes in order to avoid further confusion. We emphasize the approximating methods because they are useful in many situations.