Probability Theory with Applications

The material in this book is designed for a standard graduate course on probability theory, including some important applications. It was prepared from the sets of lecture notes for a course that I have taught several times over the past 20 years. The present version reflects the reactions of my audiences as well as some of the textbooks that I used.

Preface. List of Symbols. Background Material and Preliminaries. Independence and Strong Convergence. Conditioning and Some Dependence Classes. Probability Distributions and Characteristic Functions. Weak Limit Laws. Application to Some Statistical Estimation Problems. Stopping Times, Martingales, and Convergence. Limit Laws for Some Dependent Sequences. A Glimpse into Stochastic Processes. References. Author Index. Subject Index.