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Introduction to Stochastic Processes

Publisher: 
Dover Publications
Number of Pages: 
402
Price: 
24.95
ISBN: 
9780486497976

This is a lively introduction to the subject, focusing almost completely on Markov processes and omitting martingales and Brownian motion. The writing is very clear, and the book is loaded with examples and with exercises (selected exercises have answers in the back). The book is aimed at upper-division undergraduates, and assumes a modest knowledge of probability and a moderate knowledge of calculus, but no measure theory. The present volume is a 2013 unaltered reprint of the 1975 Prentice-Hall volume.

It starts with a brief summary of probability theory, and then two fairly in-depth chapters studying Bernoulli processes and Poisson processes as introductions to the general subject of stochastic processes. Then it covers Markov processes in much more depth. It ends with some general material on renewal theory and regenerative processes. There is also some queueing theory scattered throughout.

The book is not comprehensive, and picks and chooses which theorems to prove, but it does cover all the useful and interesting parts of the subject. I think this development works well, building up a good collection of specific examples and distributions which it then parlays into general theorems.


Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.

Date Received: 
Tuesday, January 29, 2013
Reviewable: 
Yes
Include In BLL Rating: 
No
Erhan Çinlar
Publication Date: 
2013
Format: 
Paperback
Category: 
Textbook
Allen Stenger
10/16/2014
Preface
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
Afterword
Appendix. Non-Negative Matrices
References
Answers to Selected Exercises
Index of Notations
Subject Index
Publish Book: 
Modify Date: 
Tuesday, January 29, 2013
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