First Look at Rigorous Probability Theory | 
 enlarge | Author: Jeffrey S. Rosenthal
Publisher: World Scientific Publishing Company
Category: Book
List Price: $29.00
Buy New: $25.20
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Rating:  4 reviews
Sales Rank: 148177
Media: Paperback
Edition: 2
Pages: 236
Number Of Items: 1
Shipping Weight (lbs): 1
Dimensions (in): 8.8 x 6 x 0.6
ISBN: 9812703713
Dewey Decimal Number: 519.2
EAN: 9789812703712
Publication Date: November 14, 2006
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Product Description
This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. Contents: - The Need for Measure Theory
- Probability Triples
- Further Probabilistic Foundations
- Expected Values
- Inequalities and Convergence
- Distributions of Random Variables
- Stochastic Processes and Gambling Games
- Discrete Markov Chains
- More Probability Theorems
- Weak Convergence
- Characteristic Functions
- Decomposition of Probability Laws
- Conditional Probability and Expectation
- Martingales
- General Stochastic Processes
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| Customer Reviews:
Excellent primer to use as supplement or for review March 15, 2002
40 out of 41 found this review helpful
This is a marvelous primer on measure-theoretic probability. I came across it a couple of years after taking a course based on Chung's famous text ("A Course in Prob. Theory") and found it to be an excellent book for review and remediation--that is, it helped me get a better overview of the material I had already learned and it helped me learn topics such as, say, uniform integrability, that didn't sink in too well the first time around.According to the preface, the author prepared most of the book as supplemental class notes for the benefit of his students in a course whose main text was, if I recall correctly, Billingsley's excellent "Probability and Measure". The students were so enthusiastic about the usefulness of Professor Rosenthal's supplemental info that they insisted he publish it, despite his objection that the book wasn't original enough to warrant entry into an already crowded field. Well, the students made the right call: Rosenthal's clear and concise text will, I think, help almost any student learn measure-theoretic probability more efficiently. I'd also recommend it to folks who need a concise review of measure-theoretic probability.
A gem July 17, 2007
M. Henri De Feraudy (France)
6 out of 6 found this review helpful
This is my bedside book at the present time.
It's compact, written with immense respect for the reader and even covers some
financial applications.
It's recalling the measure theory I learned as an undergraduate with the right style.
So much better than some of the "Probabilty from dummies" I have put away.
When I finish the book I hope to move on to some of the heavier books with a clear idea of where I am going.
Best Probability book ever! July 10, 2006
Thomas R. Fielden (Portland, OR USA)
7 out of 9 found this review helpful
As a graduate student in mathematics I appreciate the rigorous and no nonsense treatment of the subject. I'm am using this text to study for my Ph.D. qualifying exam in statistics. It's explaining statistics in a language I understand.
There are better, but it deserves the 5 stars. November 29, 2007
Paulo Q. Saraiva
1 out of 3 found this review helpful
This book I would recommend to prepare you to study Billingslley's Probability and Measure theory. I personally prefer Jacot and Proter's Probability Essentials, for this preparation; however, I can't underestimate this book's quality, hence the 5 stars.
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