A Probability Path

Rating:
Summary: Junk !
Review: I bought this book based on the other reviewers' comments. This book is a piece of junk ! Don't buy it and waste your money. These professors should not be allowed to write books and force it on their students.

There are better books on probability and Measure Theory. Try Marek Capinski and Ekkehard Kopp. Yes, I bought this too through Amazon.

Rating:
Summary: Excellent book !
Review: I completely agree with Gappy's review. I wish I had entered the subject with this textbook instead of Durrett's. (The only complaint is that some of the chapter ending problems have serious errors. Sometimes the given conditions do not lead to the conclusion to be proven.)

Rating:
Summary: some more details
Review: I've been reading this book along with Durrett's PROBABILITY: THEORY AND METHODS and Williams' PROBABILITY WITH MARTINGALES. I also have Billingsley's PROBABILITY AND MEASURE. All of these are good books, pitched at roughly the same level. Here are a few more specific reactions:

1) Measure theory background: Resnick & Billingsley assume no background in measure theory and interleave the relevant measure theory with probability. Durrett & Williams have appendices on measure theoretic results which cover more or less the same ground.

2) Mathematical level: Resnick is a easier than the others. He spells out lots of details in the proofs that are either left as exercises or omitted altogether in the other books. I found myself reading a statement in Resnick, asking myself why the statement was true, working out the answer easily--only to find that Resnick provided the details shortly thereafter. Sometimes this is a good thing, sometimes a little tedious.

3) Style: I'd rate Resnick below Williams and Billingsley. Williams has very elegant proofs and covers as much material as Resnick in half as much space. Billingsley is wonderfully eclectic and makes connections to lots of other areas of mathematics. Resnick is easy enough to understand, but is much more workman-like.

I think Resnick fills an important niche in this literature. I think it's a good book for teaching. I also refer to it frequently when I'm confused by something in the other books. It's thorough, relatively easy to understand, and seems to be accurate.

Rating:
Summary: A good reference for mathfinance researcher and practitioner
Review: Resnick's "A probability path" really reduce my time to grasp the measure-theoretic probability stuff. I always recommend this book to those non-math major quants (Physics,CS,... etc) who need to have a quick look into the stochastics. However; some of the proofs may be a little bit too terse that are not easy to follow. You may need more patience and some mathematical maturity!

Rating:
Summary: A good instructor!
Review: Sid Resnick provides a very readable account of probability theory. This book is more like a teacher than just a mathematics book. Resnick gives a lot of motivation for every definition and every step in the proofs. He also discusses applications of the developed theory, and gives a wealth of examples in every chapter.

One notable feature of this book, which I consider unique, is that after every definition basic facts and properties related to the definition are given in an exhaustive way. This is different than the general approach which distributes such facts into proofs, and makes it harder to follow.

Rating:
Summary: True to its word
Review: The author wrote this book with non-math graduate students in mind, and succeeded admirably. The book is readable, impeccably written, with a choice of topics that satifies most modern curricula in stochastic analysis for statisticians, operations researchers, control engineers and the like. Measure theory is included (chapter 1), and receives a less cursory treatment than in Breiman's and Durrett's textbooks. The range of topics is streamlined to the truly essential tools of probability. Most notably ergodic theorems, considered standard material by other authors (e.g. Breiman, Billingsley, Shyriaev, Durrett) are not covered. Advanced topics like CLT for martingales and brownian motion are not even mentioned. On the other side, Weak* convergence, conditional dsitribution and martingales receive very good treatment, covering material you WON'T find elsewhere (e.g. Prohorov's theorem). The level of mathematical rigor is only an epsilon less than Durrett or similar works, but the payoff is much greater readability. After a careful study of the book, the reader should be equipped with the tools needed to study advanced monographies (e.g. Karatzas and Shreve, or Dembo and Zeitouni).

In my opinion this is the perfect "support" book. Read this first to grab a hold of a specific topic; then go to somewhat more advanced book to understand the rest. Also, I believe it a very suitable textbook for self-instruction. Needless to say, it's much harder to write a book like this than a very inclusive but hard-to-read manual!

Two final pieces of information for the potential buyer. First, S.Resnick (Cornell U) is a regognized leader in the discipline of probability theory and statistics. Second, there is a "sequel" to this book "Adventures in Stochastic Processes" that you may want to check. It touches upon Markov, Renewal, Point and Diffusion Processes. It's maybe less of a masterpiece than "A Probability Path", but could be what tou are looking at...

Rating:
Summary: Measure-theoretic probability for everybody
Review: This is indeed the best probability book I have ever read. It is the only non-elementary probability book (to my knowledge) which even non-mathematicians (e.g.: economists, engineers) may find easy to read. It provides a satisfactory treatment of measure-theoretic probability, it covers a good number of topics and it provides nice and eminently readable proofs for every theorem. All mathematics books should be written like this one: there are no oversimplifications, advanced results are presented when needed, everything is carefully proved, but it never lacks of explanations, nor too much knowledge is assumed of the reader (just a bit of calculus and elementary probability). You never have to struggle to understand things, because the author does not save words or formulas, in order to make everything clear. If I could give this book ten stars, I would. It is incomparably easier to read than Williams, Jacod and Protter, Capinski and Kopp, Ash or Billingsley. I reccomend it especially to financial economists willing to study seriously stochastic processes and stochastic differential equations.