This book is a revised and expanded edition of a successful graduate andreference text. The material in the book is designed for a standard graduatecourse on pr... » 

This book is a revised and expanded edition of a successful graduate andreference text. The material in the book is designed for a standard graduatecourse on probability theory including some important applications. This newedition contains a detailed treatment of the core area of probability and bothstructural and limit results are presented in full detail. Compared to thefirst edition the material and presentation are better highlighted withseveral small and large alterations made to each chapter. Key features of thebook include Indicating the need for abstract theory even in applicationsand showing the inadequacy of existing results for certain apparently simplerealworld problems Attempting to deal with the existence problems forvarious classes of random families that figure in the main results of thesubject Providing a treatment of conditional expectations and of conditionalprobabilities that is more complete than in other existing textbooks Since thisis a textbook essentially all proofs are given in complete detail even at therisk of repetition and some key results are given multiple proofs when eachargument has something to contribute. TOCPart I. Foundations. 1. BackgroundMaterial and Preliminaries. 2. Independence and Strong Convergence. 3.Conditioning and some Dependence Classes. Part II. Analytical Theory. 4.Probability Distributions and Characteristic Functions. 5. Weak Limit Laws.Part III. Applications. 6. Stopping Times Martingales and Convergences. 7.Limit Laws for some Dependent Sequences. 8. A Glimpse of StochasticProcesses. References. Author Index. Subject Index. «