A Probability Path

A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance.

Like "Adventures in Stochastic Processes", Resnick's related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study.

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...


some more details   April 28, 2003
43 out of 45 found this review helpful

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.


excellent book   July 2, 2008
Michael R. Chernick (Holland PA)
25 out of 25 found this review helpful

Gappy has gotten it right as he usually does. As a statistician who took courses in stochastic processes from Resnick at Stanford in the mid 1970s at the beginning of his career I know that he uses rigor guided by good intuition. That is the way he teaches and that is the way he writes. I have read most of the books he has written and always enjoy them and find something new in each one.

This book is written for graduate students so it is not a text that can be handled by people with very weak mathematical backgrounds. On the other hand advanced knowledge of probability theory is not needed as Resnick builds up the methods and tools to be mathematically rigorous and yet give those who are not strongly mathematically inclined a feel for probability.


Measure-theoretic probability for everybody   April 28, 2002
Marco Taboga (Torino Italy)
24 out of 24 found this review helpful

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.


A good reference for mathfinance researcher and practitioner   December 30, 2001
17 out of 18 found this review helpful

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!