About this Title
Davar Khoshnevisan, University of Utah, Salt Lake City, UT
Publication: Graduate Studies in Mathematics
Publication Year 2007: Volume 80
ISBNs: 978-0-8218-4215-7 (print); 978-1-4704-1157-2 (online)
MathSciNet review: MR2296582
MSC: Primary 60-01; Secondary 60F05, 60F15, 60H05, 60J65
This is a textbook for a one-semester graduate course in measure-theoretic probability theory, but with ample material to cover an ordinary year-long course at a more leisurely pace. Khoshnevisan's approach is to develop the ideas that are absolutely central to modern probability theory, and to showcase them by presenting their various applications. As a result, a few of the familiar topics are replaced by interesting non-standard ones.
The topics range from undergraduate probability and classical limit theorems to Brownian motion and elements of stochastic calculus. Throughout, the reader will find many exciting applications of probability theory and probabilistic reasoning. There are numerous exercises, ranging from the routine to the very difficult. Each chapter concludes with historical notes.
Graduate students interested in probability theory.
Table of Contents
- Chapter 1. Classical probability
- Chapter 2. Bernoulli trials
- Chapter 3. Measure theory
- Chapter 4. Integration
- Chapter 5. Product spaces
- Chapter 6. Independence
- Chapter 7. The central limit theorem
- Chapter 8. Martingales
- Chapter 9. Brownian motion
- Chapter 10. Terminus: Stochastic integration