Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues.
The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference.
This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.
Table of Contents
Some Background on Probability
Some Gambling Problems
Birth and Death Processes
Reliability and Renewal
Branching and Other Random Processes
Brownian Motion: Wiener Process. Computer Simulations and Projects
Answers and Comments on End-of-Chapter Problems
References and Further Reading
Peter W. Jones is a professor and Pro Vice Chancellor for Research and Enterprise at Keele University in Staffordshire, UK.
Peter Smith is a Professor Emeritus in the School of Computing and Mathematics at Keele University in Staffordshire, UK.
Praise for the second edition:
"… a clear, easily understandable and rather short overview on stochastic processes. The different topics are motivated very well, there are many graphs and 50—theoretical and practical—examples. … the book is written very carefully … for beginners, one could not imagine a better book."
—Dominik Wied, Statistical Papers (2011) 52
"… a good resource as a textbook or as a reference to complement other literature, especially with the examples and problems provided."
—Biometrics, 67, September 2011