Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 2)

Beautifully written book that explained a lot of things to me that my professor could not. I really love the subject and it explained a lot without getting too technical too fast (which is extremely easy with Markova chains).

Received the order well in time, the book is in great condition. Totally happy with the experience and worth the money.

I am a first-year graduate student in engineering who has taken a measure theoretic probability course. I can say that this textbook is one of the least reader-friendly textbooks I have ever encountered. Proofs are extremely short and miss most of the details. This makes most of the proofs very hard/impossible to follow. I thought that Rudin Analysis is complicated to follow but at least you don't get stuck in every single section like in this textbook. Luckily, I had an opportunity to go to my professor's office hours where he filled most of the gaps. Thus, if you are looking for a textbook for self-study, this one is a terrible option. I guess that the audiences for this textbook are professors/professionals who use this textbook as a reference because if you are new to some of the material the textbook will only make you frustrated.

This is a good option as an introduction to the topic. I believe the book lacks a little bit of formalism, but perhaps it would be too lengthy if every step were to be shown. Also, there are many typos in the current edition, and this alone compromises the book's overall quality.

for a dumb math major graduate student like me, this is the best book. it explains things in an friendly, enlightening way, which makes you continue on reading through the pages. even for a probability major, this book is refreshing and full of joy.

Let me preface my review by saying that I approached this book from a graduate level engineering background. I use many of the end results of this book daily in my profession, and was hoping to get a glimpe of some of the theory behind the formulas. I was especially interested in the Monte Carlo simulation methods.I found chapters 1-3 to be fairly useful in achieving the goal of further educating myself on Markov chains, but the book after that fell quite bit short of my expectations. Perhaps my level of mathematical maturity isn't enough, or I'm the wrong audience (i.e. someone that doesn't especially care if the state-space is a countable set or if the Q Matrix is explosive), but I did find some sections of the book to be difficult to comprehend, and just ended up skipping a lot of the proofs due to lack of readability.This book could appeal to a much wider audience if the first 3 chapters spent more time discussing the theorems, and then combined chapters 4 and 5 into some fully worked out numerical examples from each of the different major areas of application.The Monte Carlo section with Hastings and Metropolis algorithms were especially disappointing, and they weren't very instructive as to how to actually implement these algorithms on a computer using a real data set, which was my main interest.

This book has two principal aims. In the first half of the book, the aim is the study of discrete time and continuous time Markov chains. The first part of the text is very well written and easily accessible to the advanced undergraduate engineering or mathematics student.My only complaint in the first half of the text regards the definition of continuous time Markov chains. The definition is introduced using the technical concepts of jump chain/holding time properties. This doesn't tie out well with the treatment of the discrete time case and may seem counter-intuitive to readers initially. However, the author does establish the equivalence of the jump chain/holding time definition to the usual transition probability definition towards the end of Chapter 2.The second half of the text deals with the relationship of Markov chains to other aspects of stochastic analysis and the application of Markov chains to applied settings.In Chapter 4, the material takes a serious jump (explosion?) in sophistication level. In this chapter, the author introduces filtrations, martingales, optional sampling/optional stopping and Brownian motion. This is entirely too ambitious a reading list to squeeze into the 40 or so pages allocated for all of this, in the opinion of this reviewer. The author places some prerequisite material in the appendix chapter.Chapter 5 is a much more down-to-earth treatment of genuine applications of Markov chains. Birth/Death processes in biology, queuing networks in information theory, inventory management in operations research, and Markov decision processes are introduced via a series of very nice toy examples. This chapter wraps up with a nice discussion of simulation and the method of Markov chain Monte Carlo.If the next edition of this book removes chapter 4 and replaces it with treatment of an actual real-world problem (or two) using genuine data sets, this reviewer would be happy to rate that edition 5 stars.

Good summary of Markov chains for someone with a thorough background in stochastic processes; however, it lacks the readability for a beginner in the subject, even one with a couple probability courses under his/her belt.