Customer Reviews

Adventures in Stochastic Processes

5 star:		(4)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

This book gives the basic essentials of stochastic processes in a rigorous yet very readable way. The standart subjects (Discrete time/continuous time Markov chains, renewal processes, Poisson processes) are treated in good detail. Some more advanced subjects (Brownian motion and general random walk) are also given.

The presentation is very organized, and the author gives many interesting (and mostly, fun to read) examples. The introductory material in chapter 1 is very detailed. Chapter 2 on discrete time MC's is excellent. (I especially enjoyed seeing the interplay between convergence of time-averages and distributions).

This book is obviously more advanced than some other texts in this area (e.g., S. M. Ross - Stochastic Processes), and it emphasizes the technicality behind the proofs a bit more. I think that after learning the basic ideas in some undergrad level course, it is easier to read. One drawback of the book is that in some places the treatment is a bit dry (e.g., in the beginning of chapter 3 - Renewal processes).

Overall, I give it 4.5 / 5 stars.

Sid Renick was an assistant professor of statistics at Stanford University in the mid 1970s when I was a graduate student there. I took advanced courses in stochastic processes from him and he was on my Ph.D. orals committee. He had a unique teaching style that comes across in all his books as well. He makes mathematics, statistics and stochastic processes come alive in his writing and he usually knows when to add a touch of humor. Professor Hayes teaches probability and stochastic processes and is clearly endorsing this text with high acclaim. That review and many of the others that show why Resnick is so popular say as much or more than what I can say in this brief review.

I am a statistics lecturer, so have read a large number of statistics text books. However, this is, without a doubt, the most innovative statistics text book I have ever seen. As well as covering the various elements of the theory of stochastic processes, including Markov chains, renewal theory, point processes, continuous time Markov chains, Brownian motion and the general random walk, Resnik provides the most entertaining exercises and worked examples I have ever come across. The subject of these exercises is Happy Harry, a rather odd character who gets migrains when people overuse the "f-word" and who has a "slightly psychotic" girlfriend (among other things).

I first discovered this textbook when I was an undergraduate, studying stochastic processes. As a student, I loved this book because when a textbook is this fun, it doesn't feel like you're doing work. As an academic, I use this book as inspiration when writing problems for my students. If my students find my questions as memorable as I found Sidney Resnick's Happy Harry questions, then maybe they will remember what I have taught them, after the exam is over.

I will give separate rate to Chapter 1, 2, 6 since I have only learned these 3 chapters in class.
Chapter 1. Preliminaries --- 5/5 very well written
Chapter 2. Markov Chains --- 6/5 superbly written
Chapter 6. Brownian Motion --- 3/5 could have been explained in a simpler way
This book is very accessible to beginners who have a good math sense, but it's not recommended for non-math major.

First off this text is very organized and a pleasant read. It is not overly wordy but not terse either. The proofs don't skip key pieces of logic but also don't hold your hand through easy concepts. In addition, Resnick adds a pleasant amount of humor throughout the text. To address the complaints that the text is not for beginners, this is likely a misunderstanding as to what the author and what the reviewer often refer to as a "beginner". When Resnick says beginner, he does not mean that anyone who has taken calculus can read this book. He is using beginner to refer to a beginner at stochastic processes. There is no question that you need a strong class in calculus based probability that covers distributions, convergence etc, and you probably also need a bit of mathematical sophistication at the level of a junior undergrad advanced calculus course. This is "beginner" or "prerequisite" material for any graduate student in the quantitative sciences and hence this text should be accessible to any student in their first semester of graduate school (or potentially even an upper level undergrad).

If you are a bit week in probability theory I would recommend getting this book and supplementing it with Ross's probability models text. Its a book full of examples and intuitive explanations. Alternating between these two books will provide a more gentle transition for "Beginners".

So why only 3 stars after such a positive review of this book? The answer is that the book is not good at doing things like bolding theorems, breaking to a new line for a definition, and has a god awful appendix, that does not contain all of the key words and ideas in the book. You really have to mark this book up with a highlighter in order for it to be a good reference book, but the problem with this is that the pages are so thin your highlighter is going to bleed through.

So its a great book, but a frustrating one to use as a reference.

In advance I would like to apologize for my poor englisch.
The book is pretty good. Not for light reading, because it is advanced probibility theory and because the book is very heavy ;).
The explanations are clear and the examples are good to understand the theory. With regard to advancement it is a standard American study book.

Good luck in your course stochastic processes,
kiss Daniëlle

This book is a very good book about stochastic process. It is both terrific for those who has already been acquainted with some of the background as well as those who learn from beginning but want a sound learning of it. This book features rigorous proofs, vivid examples and very deep intuitions. I strongly recommend this one.

I used this book in both my "introduction" to stochastic processes course as well as for a more advanced Markov chains class. The book was VERY difficult to understand, and the notation does not aid in the explanation at all. I found the material to be presented in an odd order and NOT AT ALL friendly for a beginner! The material is very dense (I think that I covered perhaps 4 chapters during the course of my two semesters using this class), and does not reconcile intuition with the proofs. The Markov chains portions of the book are more understandable than the stochastic processes portions (point processes, Poisson processes, etc). I'd suggest both books by Sheldon Ross instead (the Introduction to Probability Models for beginners and the Stochastic Processes book for a beginning graduate student or beyond). I now use my copy of this book for a doorstop.