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A Probability Path 1st ed. 1998. 3rd printing 2003 Edition

4.3 out of 5 stars 18 customer reviews
ISBN-13: 978-0817640552
ISBN-10: 081764055X
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Editorial Reviews

Review

"This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems."   ―Publications of the Int’l Statistical Institute

"A very nice introductory measure-theoretic probability textbook... The emphasis [is] on developing a broad, deeper understanding of basic probability theory, the needs of students kept specifically in mind... Students will appreciate its clear, concise, and focused presentation of the material."   ―JASA

"This book is a rather comfortable probability path leading from fundamental notions of measure theory and probability theory to martingale theory, since fundamental concepts and basic theorems are always illustrated by important examples and results of additional theoretical value."   ―Statistics & Decision

"This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics...Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications." ---Revue Roumaine de Mathématiques Pures et Appliquées

From the Back Cover

​​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.

 

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. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience. 

                                                          

This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance.... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems.

―Publications of the International Statistical Institute    

 

This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics.... Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications.

―Revue Roumaine de Mathématiques Pures et Appliquées

--This text refers to an out of print or unavailable edition of this title.
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Product Details

  • Paperback: 453 pages
  • Publisher: Birkhäuser; 1st ed. 1998. 3rd printing 2003 edition (October 16, 1999)
  • Language: English
  • ISBN-10: 081764055X
  • ISBN-13: 978-0817640552
  • Product Dimensions: 6.1 x 1 x 9.2 inches
  • Shipping Weight: 1.7 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #1,006,872 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Giuseppe A. Paleologo on November 15, 2000
Format: Paperback
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.
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By A Customer on April 28, 2003
Format: Paperback
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.
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Format: Paperback
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.
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Format: Paperback
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.
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