This clear presentation of the most fundamental models of random phenomena employs methods that recognize computer-related aspects of theory. The text emphasizes the modern viewpoint, in which the primary concern is the behavior of sample paths. By employing matrix algebra and recursive methods, rather than transform methods, it provides techniques readily adaptable to computing with machines.
Topics include probability spaces and random variables, expectations and independence, Bernoulli processes and sums of independent random variables, Poisson processes, Markov chains and processes, and renewal theory. Assuming some background in calculus but none in measure theory, the complete, detailed, and well-written treatment is suitable for engineering students in applied mathematics and operations research courses as well as those in a wide variety of other scientific fields. Many numerical examples, worked out in detail, appear throughout the text, in addition to numerous end-of-chapter exercises and answers to selected exercises.
Table of Contents
1. Probability Spaces and Random Variables
2. Expectations and Independence
3. Bernoulli Processes and Sums of Independent Random Variables
4. Poisson Processes
5. Markov Chains
6. Limiting Behavior and Applications of Markov Chains
7. Potentials, Excessive Functions, and Optimal Stopping of Markov Chains
8. Markov Processes
9. Renewal Theory
10. Markov Renewal Theory
Appendix. Non-Negative Matrices
Answers to Selected Exercises
Index of Notations