Product Description

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.

Product Details

• Amazon Sales Rank: #1911305 in Books
• Published on: 1999-11-29
• Original language: English
• Number of items: 1
• Binding: Paperback
• 250 pages

Customer Reviews

A pedagogical introduction to modern probability theory.
This book can be seen as a simplified and pedagogical version of the respective authors longer and authoritative treatises on stochastic processes. It contains the prerequisites for a graduate courses on diffusion processes or stochastic differential equations and gives a clear exposition of the main notions of probability theory needed for these more advanced topics. The main difference with standard treatises on stochastic processes is that the authors give a motivation for each new definition and state the relation between the new notions introduced: a good example is the very clear exposition in Chapters 17 and 18 of different notions of convergence for random variables or the construction of probability measures in Chapters 6 and 7. Of course the notions of "essentials" depends on what one has in mind and here, the choice seems to have in mind a reader heading towards a graduate course on stochastic calculus or diffusion proceses, hence the final chapters on martingale inequalities and supermartingales. However, material on a useful and 'essential' topic such as Poisson processes is omitted, since the book chooses to deal with random variables and not stochastic processes. Also, (discrete time) martingales are introduced not as particular examples of stochastic processes but as a class of sequences of random variables in which the central limit theorem continues to hold.

The book is not written in theorem-proof format and is therefore readable. Each chapter contains example and explanations, which is nice. However the examples are theoretical and no real-life examples are included. So the book should be more appealing to a student with a taste for mathematics and well versed in a branch of mathematics other than probability rather than an engineering or business student. Overall: one of the best mathematical textbooks on modern probability theory written to this day.

Overall dry but otherwise rigorous treatment
Altough the book covers probability from the measure point of view in some detail, I found that is quite difficult to read as textbook, i.e. from page 1 to the end. I would prefer some more peadagogical treatment of some of the more difficult subjects, i.e conditional expectation, rather than the "Lemma-Proof" type of approach, which nevertheless is required for such a subject.

It requires decent exposure to some measure concepts and to some probability concepts as well. On the positive side, it very rigorous from a mathematical point of view and quite complete as a book.

I would recommend buying it, but more than a reference rather than a textbook.