This is a must book for engineers, scientists, and engineering managers. Garvey's book presents how probability theory is applied to model, measure, and manage risk in the cost of a systems engineering project. The work is a first of its kind in the engineering, cost engineering/analysis, and operations research communities.

The book provides readers a clear discussion on the nature of uncertainty, how it affects the cost of a systems engineering project, and how probability methods are used to model, measure, and control risk from a systems engineering perspective. Readers benefit from the numerous mathematical and professional anecdotes, case discussions, results, observations, and interpretations found throughout the chapters.

The book contains 110 applied and theoretical exercises. It is an outstanding text for students in engineering and the related fields.

Rick Durrett was a graduate student in operations research at Stanford. Rick was Iglehart's prize student and was even then predicted to surpass Iglehart in his achievements.

Rick has been an academic his entire career and has made major contributions in applied probability. He also explains things in very intuitive ways and has thus been able to publish a number of successful books on various aspects of probability theory and stochastic processes. In this book Rick presents a variety of probability models to explain the evolution of DNA sequences that are found in humans. This represents an interesting and important area of research that has tremendous impact on medical treatments, pharmaceuticals and genetic engineering. Most of all it has the rigorous touch that Rick always gives to his work.

If you are looking for an excellent investment book that gives you the facts this is it. Moshe uses past performance and a Monte Carlo simulation program to 'weigh the odds' on which investments perform better than other investments and more importantly over what time horizon. A good book to go along with this is Nick Murray's book Simple Wealth Inevitable Wealth. If you are a broker like my self this will help you understand how to help your clients. If you are an investor this is a great book for you to truly understand what investing is all about and what risk really is - cause it ain't a basket of stocks - it's purchasing power.

(This review is based on the second Russian edition printed in 1986. The contents of English edition seems to be a bit extended version of the Russian one.)

This is a very good exposition to probability theory at the professional level. I like it much more than I do Billingsley's "Probability and Measure" (which is a collection of essays on probability theory, sometimes only vaguely related a few chapters apart from each other, while Borovkov is a very consistent course which has the same level of rigor as Billingsley does, and which also proves some subtle but appreciable things not mentioned in Billingsley). It has a bit different flavor of tending to prove things via characteristic functions rather than directly with the cesnored random variables as in Billinsley's book. It does not cover as much measure theory as Billingsley does, and I suspect that the book implicitly assumes the student to be familiar with a standard Russian reference on functional analysis by Kolmogorov and Fomin that has an extensive treatment of Lebesgue integration. It is also nice that it has a lot of examples discussed in the text (rather than given as exercises) that help to cement the concepts. They make the text quite lively, too. Sometimes I had to spend a minute or two thinking why they believe a statement in a proof is self-evident, though.

The book starts with with the introduction of probability spaces, goes on to random variables, then to the laws of large numbers, convergence notions, and the CLTs. It also discusses renewal theory, factorization identities, Markov chains, information and entropy, martingales, continuous time stocastic processes, functional limit theorems, and Markov processes, with some measure theory stuff and a couple of more difficult theorems (extension of a measure, Kolmogorov theorem on consistent distributions, theorems of Helly and Arcela--Ascoli) given in appendices. Thus it covers more than a semester of probability theory, giving some initial reading for some four or so advanced courses. The author suggests to use the bulk of the material in the first ten or twelve chapters for a required semester course, with the rest of the book viewed as the material for shorter elective courses. The book helped me greatly in my probability theory comprehensive exam, as well as in my stochastic calculus and stochastic processes courses.

It is a pity that the book is rather expensive -- I am happy to have it in the original language on which this review is actually based.

Of historical interest it is that A.Borovkov is Kolmogorov's student.

My special field is neither statistics nor math. My reading this book was for research purpose. I enjoyed reading it, though it contains a few of "printing" mistakes.

The chapter 6 is somehow hard-to-find. I believe Talagrand's isoperimetric theory has wide range of applications. But it is not easy to read his original article (which, besides, is more than 100-page long). The chapter gives a very informative introduction to the theory.

In recent years many excellent graduate textbooks in probability have become available. Although these books provide the reader with the basic analytic tools of measure theoretic probability, they usually fall short of presenting probability in more general (and abstract) spaces. As far as I know, there are not many good books on the subject: Billingsley "Convergence of Probability Measures" comes to mind, and Jacod and Shiryaev's "Limit Theorems for Stochastic Processes" (both excellent, and very expensive). The goal of this booklet is to fill this void and to provide a researcher with some more advanced analytical tools. The book is a "selection of topics" in the author's words, and I think it has no pretense of completeness. What it presents, it presents very well, with short yet rigorous proofs (as far as I can tell: I studied only the first two chapters, and the last one). The reader should know probability at least at the level of Billingsley's "Probability and Measure". A basic command of topological spaces and Banach spaces is recommended. One criticism: having a PhD student in mind, the author could have spent a few more pages on examples, but this doesn't detract much from a book that is already a helpful reference and an example of good style.
Finally, here are the titles of the chapters, with a short description when needed: 1. Introduction [sets the stage for random variables in Polish spaces] 2. Spaces of probability measures 3. Conditioning and martingales 4. Basic limit theorems [SLLN, CLT, LIL, Large Deviations] 5. Markov chains 6. Foundations of continuous time processes.

Doing problems is the best way to study mathematics. The question to most authors is that: How to select problems that are nice to the students. This book did quite well. As I see, the authors gave the exact right pace to offer the students an exicting course, and give the students a thorough understanding.

If you want to master this subject in a month, or even in a shorter time, this book may be the right choice.

Each paragraph leads into the next with examples and review of probability concepts. After awhile, you'll discover that you've learned quite a bit without even noticing it, as the book is seamless.

Perfect for poker players or anyone who wants to learn how to figure odds. I can't recommend it enough. It was just what I was looking for.

This book is suitable for my graduate studies on computer performance. The author directs us from combinatorics, distribution theory, queue theory to queueing networks in a systematic way. I have read the book at ease for its stepwise elaboration of concepts. However, I have also read with hardship as it requires the readers to possess a good command of mathematics, both pure and applied, in order to go through the book.

For a mathematics graduate studying computer networks, I recommend this book. A novice or a mediocrity should pay more patience to read if not yet at a loss.

This book has aroused my interest and eagerness to know more about computer performance from the viewpoint of queueing and networking. In a word, I enjoy reading this book.

This is a great book to teach 2nd/3rd grade basic probability. Kids love the pictures and the story line is too cute! A great book to integrate language arts and math.