Customer Reviews

Finite Markov Chains: With a New Appendix "Generalization of a Fundamental Matrix" (Undergraduate Texts in Mathematics)

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I have been familiar with this book for over 8 years and I should say this is one of the best educational and practical books you can find about Markov chains. The book claims to be written for undergraduates, but it is marvelously useful for graduate students too.

The book starts by definition of Markov chains and gradually gets into more advanced definitions like absorbing states, cyclical chains, ergodicity ... Then there are these little lemmas and theorems about different aspects of Markov chains like what is the expected time of sitting at a transient state, what is the expected time of returning to the same state, etc. The proofs are nicely presented and there is a whole lot of application for those theorems in all fields that use Markov chains (like engineering, economics, ...). The book is actually abstract math and doesn't get very specialized at any time.

I think this is a book one wants to start learning Markov chains from or keep in shelf for frequent references. I actually used some of its derivations in my own Master's thesis and got a lot of interesting feedbacks on what I did. Now is your turn!