A First Look At Rigorous Probability Theory

“This is a fine textbook on probability theory based on measure theory. The parts of measure theory that are needed are developed within the book and a teacher of measure theory could find them quite useful. The construction of the Lebesgue measure (extension theorem) is unusual and interesting.” Mathematical Reviews “This short, lucid and excellent textbook should be a required course for all graduate students of mathematics and statistics as well as for interested graduate / PhD students in engineering, computer sciences, economics, and management who lack exposure to measure theoretic applications in probability theory.” Professor B K Sahu Indian Institute of Technology, India Solutions Manual for Free Download This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.

Table of Contents

1 The need for measure theory

2 Probability triples

3 Further probabilistic foundations

4 Expected values

5 Inequalities and convergence

6 Distributions of random variables

7 Stochastic processes and gambling games

8 Discrete Markov chains

9 More probability theorems

10 Weak convergence

11 Characteristic functions

12 Decomposition of probability laws

13 Conditional probability and expectation

14 Martingales

15 General stochastic processes

A. Mathematical Background

B. Bibliography