A Probability Path by Sidney Resnick (PDF)

Description

Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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%.

⭐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.

⭐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 content of the book is excellent, my problem is with the very poor quality of the print on demand reproduction. I could get a better quality of print if I took the book I borrowed from the library and photocopied it myself. The print on demand copy I was sent has print which is thick, blurred and very shiny, which makes it much harder to read.The real question I have is why would anyone willing pay full price for such a poor quality photocopy. The real issue is that you is not told that you are going to be sent a crappy photo copy rather than a properly printed book.I wish to be told that I will get a print on demand book so that I can choose to avoid such poor quality print.

⭐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.

⭐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…

⭐I thoroughly enjoyed reading this book. The main reason I don’t give it 5 stars is because the chapter on Integration and Expectation skips some important relationships between Fubini and the counting measure which could help us in some cases for the interchange between a sum and integration… Also, the author doesn’t have an up to date errata available anywhere.

⭐a solid math background is helpfula fast paced text

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