Probability Essentials

by Jean Jacod, Philip Protter

This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.

Genres: Mathematics

264 pages, Paperback

First published November 30, 1999

Reviews

[Evan · Rating 5 out of 5]

Now that's a nice book to take with you to the pool and relax on a hot summer day! All those nice reads!! Highly recommended if you feel guilty with your Ph.D. research, and you want to freshen-up on your measure-theoretic probability (don't we all??)

[Kai · Rating 4 out of 5]

clear exposition

[Alireza Daneshvar · Rating 3 out of 5]

For a review of pure probability basics, this book is a good choice.

[Daniel · Rating 5 out of 5]

Fills a needed niche between extensive electrical-engineering undergrad style probability and more graduate type measure theoretic stochastic processes literature.

[Emanuel · Rating 3 out of 5]

I used this book for two courses at my university. It has the amazing property of actually covering most essentials of probability within a reasonable time frame (even considering the exercises). However, this comes at a very steep cost.

Some parts of the book are outright wrong—so much so that the university had to hand out a 20-page PDF with caveats, additions to the literature, and corrections of the material. It is sad, since it has captured the essence of 'essentials' really well. Its execution was just very lacking. Trying to come up with ideas on how to fix this is probably futile. The last edition was made in 2002, so there likely will not be any corrections made.

None of the following books can do the exact same thing as Probability Essentials, but sometimes the price is just not worth paying.

If you want to review the very basics of probability theory, then I would recommend you to work problems in Blitzstein, J. K., & Hwang, J. (2019). Introduction to Probability. CRC Press, Taylor & Francis Group. Keep in mind this book is quite long, but it has summaries in each chapter and many great exercises to work with.
If you want to review the basics of measure theory, then I would recommend you skim through Schilling, R. L. (2017). Measures, Integrals and Martingales. Cambridge University Press. This book is a monster, but very thorough with solutions to all problems.
If you just want to cover essentials, then I would recommend you to read some of Schilling, R. L. (2021). Measure, Integral, Probability & Process. Technische Universität Dresden. This book is truly dense and captures the essentials of the entirety of probability, but without any exercises.

Edit: There was a corrected printing done in 2004–this is actually the version I'm talking about above. I realise in hindsight, that some of the above is a bit imprecise–I hope that the general message gets through.

[Lokprakash]

Good read Probability Essentials