A Probability Path (Modern Birkhäuser Classics)

The book is true to its word, as many other reviews have already testified. I entered a graduate level probability class with a math bachelors background, and with only one semester of real analysis under my belt, I was pretty overwhelmed. We used Kai Lai Chung's A Course in Probability Theory, which assumes a fairly high comfort level in such mathematics. Resnick's book proved to be a perfect companion to Chung's book, and made a world of difference in my understanding of probability. Resnick spells things out more explicitly, starts from the ground up, and often comments on the utility, or the "why is this important," of certain results, the big picture if you will.

The author is very far off of the supposed "probability for all fields (not just mathematicians)" goal. The readings are great, but the problems assume far more familiarity with measure theory than what the author claims. Pair this book with Rene Schillings measure theory text. Read the sections here, then go read the equivalent section and do the problems in Schillings book.

It's really a great book. The shipping is fast, and the package is well taken care of. The book itself is absolutely brand new. I like it. Thanks!

great book

For me this book is one of those I wish I never bought. I bought the book because it aims to provide an introduction to probability theory with measure theory and still not be geared only towards mathematicians. The book style is however the usual Definition/Theorem/Proof/Example style without much motivation, explanantion (besides the proofs) and application.

This is a good book for a theoretical, analysis-based look at probability measure theory. If you haven't had any measure theory or analysis before, you may find it a bit hard to read. There is a good deal of hand-waving in the book (more so than most other texts). If you're using this book for a course, I definitely recommend a supplemental analysis book.

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 distribution 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...

This is a great, high-quality book although it has some shortcomings. Overall I prefer Billingsley - Probability and Measure.Pros* The intro to mathematical finance at the end (sec 10.16) is really cool. You'll be excited to read about applications of the theoretical material.* Lots of exercises* Rigorous proofs* Readable styleCons* Chapter 7 on the law of large numbers presents an unnecessarily awkward proof. Definitely follow Chung - A Course in Probability Theory instead (or read about ergodic theorems)* Billingsley - Probability and Measure gives more useful background about Radon-Nikodym densities than this book does.* No solutions to exercises.Neutral* This book often includes material here and there that is beyond the core topics. Most courses would include 70%-90%.

a solid math background is helpfula fast paced text