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31 people found this helpful

ByM. Henri De Feraudyon August 18, 2009

As far as beginning graduate-level books on probability are concerned this is definitely one of the best. This looks like a set of lectures turned into a book.

The competition in my mind would be

First Look at Rigorous Probability Theory (more compact, perhaps a little dense)

Probability & Measure Theory, Second Edition (covers more ground and is very clear)

A Course in Probability Theory, Revised Edition, Second Edition(very detailed explanations, but you should probably have followed a course on measure theory)

Please dont dive into probability at this level, your intuition might not be ready for it.

To do that I recommend

An Introduction to Probability Theory and Its Applications, Vol. 1 (Volume 1) (if you have the time)

There is also Basic Probability Theory (Dover Books on Mathematics) which is an excellent introduction stopping short of measure theory.

The competition in my mind would be

First Look at Rigorous Probability Theory (more compact, perhaps a little dense)

Probability & Measure Theory, Second Edition (covers more ground and is very clear)

A Course in Probability Theory, Revised Edition, Second Edition(very detailed explanations, but you should probably have followed a course on measure theory)

Please dont dive into probability at this level, your intuition might not be ready for it.

To do that I recommend

An Introduction to Probability Theory and Its Applications, Vol. 1 (Volume 1) (if you have the time)

There is also Basic Probability Theory (Dover Books on Mathematics) which is an excellent introduction stopping short of measure theory.

3 people found this helpful

ByCJRon July 4, 2012

The opening chapters (1-6) provide a decent and readable introduction to key concepts in measure theory: sigma-algebras, (probability) measures, random variables, etc. However, the middle and later chapters are written like lecture notes --definition, theorem, proof; theorem proof; theorem, proof, corollary -- with little motivation or explanation of relevance to measure theoretic probability, i.e. the lecturer would provide such motivations and explanations (unfortunately the book does not come with a lecturer). The chapters on martingales are thorough--but read like a reference rather than a text-- and the token chapter on the Radon-Nikodym theorem fails to capture its importance in measure theoretic probability. Overall, this book serves as a decent introduction, but I would recommend supplementing the material with corresponding material from e.g. Ash's Probability and Measure Theory or Billingsley's Probability and Measure.

ByM. Henri De Feraudyon August 18, 2009

As far as beginning graduate-level books on probability are concerned this is definitely one of the best. This looks like a set of lectures turned into a book.

The competition in my mind would be

First Look at Rigorous Probability Theory (more compact, perhaps a little dense)

Probability & Measure Theory, Second Edition (covers more ground and is very clear)

A Course in Probability Theory, Revised Edition, Second Edition(very detailed explanations, but you should probably have followed a course on measure theory)

Please dont dive into probability at this level, your intuition might not be ready for it.

To do that I recommend

An Introduction to Probability Theory and Its Applications, Vol. 1 (Volume 1) (if you have the time)

There is also Basic Probability Theory (Dover Books on Mathematics) which is an excellent introduction stopping short of measure theory.

The competition in my mind would be

First Look at Rigorous Probability Theory (more compact, perhaps a little dense)

Probability & Measure Theory, Second Edition (covers more ground and is very clear)

A Course in Probability Theory, Revised Edition, Second Edition(very detailed explanations, but you should probably have followed a course on measure theory)

Please dont dive into probability at this level, your intuition might not be ready for it.

To do that I recommend

An Introduction to Probability Theory and Its Applications, Vol. 1 (Volume 1) (if you have the time)

There is also Basic Probability Theory (Dover Books on Mathematics) which is an excellent introduction stopping short of measure theory.

A Kid's Reviewon October 3, 2000

This is an excellent and timely textbook on probability and martingale theory. There is an increasing need of thorough but concise treatise of probability theory for researchers and graduate students in Engineering, Economics, Statistics and Mathematical Biology. Very few textbook fill this need. Jacod and Protter succeeded in bringing together essential concepts and theorems in probability/martingale theory in a clear and lucid style and the book is completely self-contained: all necessary machinery from measure theory are explained and proved while providing a flavor of probabilistic way of thinking. Unlike Williams' "Probability with Martingales", all mathematical details are covered in the body of text. They present conditional expectation through Hilbert space approach and Radon-Nikodym theorem is proved at the end of the book using martingales. This is an indoctrinated way of showing how martingales are applied in other field of mathematics. Each chapter starts with pedagogical explanation of concept and summary of results. This helps reader grasp concepts and develop intuition. The topics, examples and exercises are carefully chosen and well organized. I found several but minor typos and discrepancy in the notation during the last five chapters. Yes, elegant proof is given for each theorem on martingales but rephrasing them may help make it clear where in the proof previous results are used and applied. Also, it would be a great idea to include introductory texts on stochastic calculus in the reference for the beginning students. Despite these minor suggestions, I recommend the book with enthusiasm. After reading this book, one can take their way immediately to stochastic calculus: Brownian motion and Ito calculus and their applications.

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ByCJRon July 4, 2012

The opening chapters (1-6) provide a decent and readable introduction to key concepts in measure theory: sigma-algebras, (probability) measures, random variables, etc. However, the middle and later chapters are written like lecture notes --definition, theorem, proof; theorem proof; theorem, proof, corollary -- with little motivation or explanation of relevance to measure theoretic probability, i.e. the lecturer would provide such motivations and explanations (unfortunately the book does not come with a lecturer). The chapters on martingales are thorough--but read like a reference rather than a text-- and the token chapter on the Radon-Nikodym theorem fails to capture its importance in measure theoretic probability. Overall, this book serves as a decent introduction, but I would recommend supplementing the material with corresponding material from e.g. Ash's Probability and Measure Theory or Billingsley's Probability and Measure.

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BySe Winvictaon October 30, 2015

This is Springer's attempt at Cliff's Notes? As others have pointed out, it is essentially a set of summary notes, not a real book. At a price level just a little higher, you can get much better ones.

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ByMatthiason March 23, 2014

the statistics lecturer at my university recommended this book, and they choose to purchase it for my studies. The book holds a lot of information, and is definitely worthwhile for those who are interested in numbers. Formulas are well explained and properly documented through methodical examples.

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ByAlgernop Kriegeron July 22, 2014

This book is my favorite to use as a basis for an introduction to probability theory course. It’s graduate-level material designed to give a rigorous basis for later probability based courses, and it succeeds admirably. The presentation is clear, detailed, and structured in a way that it is fairly easy to design a course around the book—one can make it a required textbook or just use it as a guide to form lecture notes. The same clear exposition and sufficient detail enables it to be used as a self-study guide, too, as long as one has a reasonably rigorous background in mathematics.

It’s a bit slim and lecture/lesson-oriented to be that great as a reference book, but it’s great to build a course around, and not overly expensive for students. Highest recommendation.

It’s a bit slim and lecture/lesson-oriented to be that great as a reference book, but it’s great to build a course around, and not overly expensive for students. Highest recommendation.

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ByDuzhe Wangon August 4, 2015

Very good. Awesome.

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A Kid's Reviewon October 3, 2000

This is an excellent and timely textbook on probability and martingale theory. There is an increasing need of thorough but concise treatise of probability theory for researchers and graduate students in Engineering, Economics, Statistics and Mathematical Biology. Very few textbook fill this need. Jacod and Protter succeeded in bringing together essential concepts and theorems in probability/martingale theory in a clear and lucid style and the book is completely self-contained: all necessary machinery from measure theory are explained and proved while providing a flavor of probabilistic way of thinking. Unlike Williams' "Probability with Martingales", all mathematical details are covered in the body of text. They present conditional expectation through Hilbert space approach and Radon-Nikodym theorem is proved at the end of the book using martingales. This is an indoctrinated way of showing how martingales are applied in other field of mathematics. Each chapter starts with pedagogical explanation of concept and summary of results. This helps reader grasp concepts and develop intuition. The topics, examples and exercises are carefully chosen and well organized. I found several but minor typos and discrepancy in the notation during the last five chapters. Yes, elegant proof is given for each theorem on martingales but rephrasing them may help make it clear where in the proof previously results are used and applied. Also, it would be a great idea to include introductory texts on stochastic calculus for the beginning students. Despite these minor suggestions, I recommend the book with enthusiasm. After reading this book, one can take their way immediately to stochastic calculus: Brownian motion and Ito calculus.

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ByHyun Jin Sonon October 2, 2014

Good

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