Introduction to Stochastic Processes

✍ Scribed by Erhan Cinlar

• Publisher: Dover Publications
• Year: 2013
• Tongue: English
• Leaves: 418
• Series: Dover Books on Mathematics
• Edition: Illustrated
• Category: Library

✦ Synopsis

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

Copyright
Contents
Preface
Chapter 1 - Probability Spaces and Random Variables
Chapter 2 - Expectations and Independence
Chapter 3 - Bernoulli Processes and Sums of Independent Random Variables
Chapter 4 - Poisson Processes
Chapter 5 - Markov Chains
Chapter 6 - Limiting Behavior and Applications of Markov Chains
Chapter 7 - Potentials, Excessive Functions, and Optimal Stopping of Markov Chains
Chapter 8 - Markov Processes
Chapter 9 - Renewal Theory
Chapter 10 - Markov Renewal Theory
Afterword
Appendix - Non-Negative Matrices
References
Answers to Selected Exercises
Index of Notations
Subject Index