Probability Theory

This work presents a rigorous exposition of probability theory for a variety of applications. The first part of the book is a self-contained account of the fundamentals. Material suitable for advanced study is then developed from the basic concepts. Emphasis is placed on examples, sound interpretation of results and scope for applications. A distinctive feature of the book is that it discusses modern applications like risk theory, stochastic optimization and comparison of distributions, seldom covered in traditional texts. The book also includes some recent developments on limit theorems for sums of dependent variables, and nonlinear and nonclassical limit theorems. Simplified proofs and a unified approach to the exposition of many results are other key features. The book may be used as a textbook for graduate students and advanced undergraduates, and as a work of reference. This book presents a rigorous exposition of probability theory for a variety of applications. The first part of the book is a self-contained account of the fundamentals. Material suitable for advanced study is then developed from the basic concepts. Emphasis is placed on examples, sound interpretation of results and scope for applications.A distinctive feature of the book is that it discusses modern applications seldom covered in traditional texts. Two cases in point are risk theory (or comparison of distributions) and stochastic optimization. The book also includes some recent developments of probability theory, for example limit theorems for sums of dependent variables, nonlinear and nonclassical limit theorems. Simplified proofs and a unified approach to the exposition of many results are other key features.The book may be used as a textbook for graduate students and advanced undergraduates, and as a work of reference. This work presents an exposition of probability theory for a variety of applications. It starts with an account of the fundamentals, then develops material suitable for advanced study. Emphasis is placed on examples, sound interpretation of results and scope for applications. This chapter deals with basic concepts of probability theory such as probability distribution, random variable and its mean (expectation).