Probability Essentials (Universitext) [Paperback]

Jean Jacod (Author), P. Protter (Author), J. Jacod (Author), Philip E. Protter (Author)

Book Description

ISBN-10: 354066419X | ISBN-13: 978-3540664192 | Publication Date: December 1999

This introduction to "probability theory" can be used, at the initial graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course. It should be useful for students and teachers in related areas such as finance theory (economics), electrical engineering and operations research. The text covers the essentials with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it should bring them from a starting knowledge of the subject to a knowledge of the basics of Martingale theory. After learning probability theory from this text, the student should be ready to continue with the study of more advanced topics, such as Brownian motion and Ito calculus, or statistical inference.

Editorial Reviews

Review

"(The book is) a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises. ... The authors make it clear what luggage is required for this exhilarating trek,... a good knowledge of advanced calculus, some linear algebra, and some "mathematical sophistication". With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job." The Mathematical Gazette, Vol. 84, No 500, 2000 "The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. ... Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience." Short Book Reviews, Vol. 21, No. 2, 2001 --This text refers to an alternate Paperback edition.

Product Details

• Paperback: 250 pages
• Publisher: Springer-Verlag (December 1999)
• Language: English
• ISBN-10: 354066419X
• ISBN-13: 978-3540664192
• Product Dimensions: 9.3 x 6.2 x 0.6 inches
• Shipping Weight: 11.2 ounces
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #4,103,999 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

24 of 27 people found the following review helpful:

4.0 out of 5 stars All background needed for Ito calculus is here, October 3, 2000

A Kid's Review

This review is from: Probability Essentials (Universitext) (Paperback)

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.

12 of 12 people found the following review helpful:

5.0 out of 5 stars Excellent graduate introcuction, August 18, 2009

By 

M. Henri De Feraudy (France) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Probability Essentials (Paperback)

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.

10 of 17 people found the following review helpful:

4.0 out of 5 stars All backgound needed for Ito calculus is here!, October 3, 2000

A Kid's Review

This review is from: Probability Essentials (Universitext) (Paperback)

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.