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Introduction to the Numerical Solution of Markov Chains,New
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A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuseand applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field.Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discretetime and continuoustime Markov chains and examines many different numerical computing methodsdirect, singleand multivector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.
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- Q: What is 'Introduction to the Numerical Solution of Markov Chains' about? A: This book provides a systematic and detailed treatment of the numerical solution of Markov chains, exploring their applications in fields like engineering, computer science, economics, and education.
- Q: Who is the author of the book? A: The author is William J. Stewart, who is known for his contributions to applied probability and Markov chains.
- Q: What are the key features of this book? A: The book is a hardcover edition with 568 pages and is classified as a used book in good condition.
- Q: When was the book published? A: It was published on November 14, 1994.
- Q: What topics are covered in the book? A: The book covers various numerical computing methods for Markov chains, including direct, iterative, and projection methods, as well as transient solutions and stochastic automata networks.
- Q: Is this book suitable for beginners? A: While it provides extensive background, it is best suited for readers with some prior knowledge in applied probability and numerical methods.
- Q: What makes this book essential reading? A: It offers a detailed exploration of numerical solutions for Markov chains, making it valuable for scientists and professionals in rapidly growing fields.
- Q: Does the book include practical examples? A: Yes, throughout the text, Stewart includes numerous examples and comparisons among different numerical methods.
- Q: What is the edition of this book? A: This is the first edition of 'Introduction to the Numerical Solution of Markov Chains'.
- Q: Are there any software recommendations in the book? A: Yes, the book includes discussions on currently available software for computing solutions of Markov chains.