A Graduate Course in Probability

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini's theorem, Radon-Nikodym theorem, Egorov's theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work. Content: Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Page ii Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Pages vii-ix CHAPTER 1 - Probability Spaces, Pages 1-14 CHAPTER 2 - Probability Distributions, Pages 15-56 CHAPTER 3 - Stochastic Independence, Pages 57-76 CHAPTER 4 - Basic Limiting Operations, Pages 77-106 CHAPTER 5 - Strong Limit Theorems for Independent Random Variables, Pages 107-146 CHAPTER 6 - The Central Limit Theorem, Pages 147-208 CHAPTER 7 - Conditional Expectation and Martingale Theory, Pages 209-244 CHAPTER 8 - An Introduction to Stochastic Processes and, in Particular, Brownian Motion, Pages 245-269 Suggested Reading, Page 270 Index, Pages 271-273