Hardcover ISBN:  9781470409074 
Product Code:  GSM/149 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $64.00 
Electronic ISBN:  9781470410278 
Product Code:  GSM/149.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $60.00 

Book DetailsGraduate Studies in MathematicsVolume: 149; 2013; 284 ppMSC: Primary 60;
This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones.
The book is a selfcontained introduction to probability theory and the measure theory required to study it.ReadershipGraduate students and researchers interested in probability.

Table of Contents

Chapters

Chapter 1. Some background and preliminaries

Chapter 2. Probability theory on uncountable sample spaces

Chapter 3. Some applications to probability theory

Chapter 4. The central limit theorem and Gaussian distributions

Chapter 5. Discrete parameter stochastic processes

Chapter 6. Some continuoustime processes

Chapter 7. Martingales


Additional Material

Reviews

... I regard this book highly, and I recommend it for course use as well as for independent study.
MAA Reviews 
This book is a very thorough advanced undergraduate/beginning graduate course on probability theory for students who have a good background in modern mathematical ideas. ... [W]hat distinguishes this book from its many competitors is the thoroughness of argument, and the tasteful choice of auxiliary topics that complement the main menu. ... The book is replete with carefully chosen exercise for readers to test their understanding. Another nice touch is that the author always takes care to let the reader know who originally came up with a particularly clever argument or method. In this way, readers get a healthy exposure to ways of thinking originating from Doeblin, Doob, Dynkin, Huygens, Kac, Kolmogorov, Livy, Marcinkiewicz and Wiener, among many others. This is a very good book on which to base a graduate course or to use for selfstudy.
David Applebaum, University of Sheffield, South Yorkshire, UK 
Mathematics of Probability is a very enjoyable book. It is definitely a book for graduate students, but it manages to begin exploring the subject without a lot of prerequisites. ... It manages to discuss rigorously, and in a mostly selfcontained manner, advanced topics which are not found in undergraduate books. ... It is a good book for independent study. It does not overwhelm the reader with exercises (each section ends with several problems). The footnotes and the comments at the end of each chapter are to the point and help the reader keep focus. ... All in all, I regard this book highly and I recommend it for course use as well as for independent study.
Florin Catrina, MAA Reviews


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This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones.
The book is a selfcontained introduction to probability theory and the measure theory required to study it.
Graduate students and researchers interested in probability.

Chapters

Chapter 1. Some background and preliminaries

Chapter 2. Probability theory on uncountable sample spaces

Chapter 3. Some applications to probability theory

Chapter 4. The central limit theorem and Gaussian distributions

Chapter 5. Discrete parameter stochastic processes

Chapter 6. Some continuoustime processes

Chapter 7. Martingales

... I regard this book highly, and I recommend it for course use as well as for independent study.
MAA Reviews 
This book is a very thorough advanced undergraduate/beginning graduate course on probability theory for students who have a good background in modern mathematical ideas. ... [W]hat distinguishes this book from its many competitors is the thoroughness of argument, and the tasteful choice of auxiliary topics that complement the main menu. ... The book is replete with carefully chosen exercise for readers to test their understanding. Another nice touch is that the author always takes care to let the reader know who originally came up with a particularly clever argument or method. In this way, readers get a healthy exposure to ways of thinking originating from Doeblin, Doob, Dynkin, Huygens, Kac, Kolmogorov, Livy, Marcinkiewicz and Wiener, among many others. This is a very good book on which to base a graduate course or to use for selfstudy.
David Applebaum, University of Sheffield, South Yorkshire, UK 
Mathematics of Probability is a very enjoyable book. It is definitely a book for graduate students, but it manages to begin exploring the subject without a lot of prerequisites. ... It manages to discuss rigorously, and in a mostly selfcontained manner, advanced topics which are not found in undergraduate books. ... It is a good book for independent study. It does not overwhelm the reader with exercises (each section ends with several problems). The footnotes and the comments at the end of each chapter are to the point and help the reader keep focus. ... All in all, I regard this book highly and I recommend it for course use as well as for independent study.
Florin Catrina, MAA Reviews