| Author | Wai-Ki Ching, Michael K. Ng |
| Publisher | Springer |
| Year | 2006 |
| Language | English |
| Pages | 205 |
| Size | 1.41 MB |
| Extension |
Summary
Markov Chains: Models, Algorithms and Applications is a comprehensive monograph that systematically explores the theory, computational methods, and practical uses of Markov chains. The book is designed for students, researchers, and professionals in applied mathematics, operations research, scientific computing, and related fields. It begins with a solid foundation in both discrete-time and continuous-time Markov chains, including their relationship with matrix theory, before progressing to more advanced topics such as higher-order models, multivariate chains, and hidden Markov models.[reference:0][reference:1]
Each chapter is dedicated to a specific model class or application area, with a strong emphasis on numerical algorithms that can efficiently solve the models. The book covers a wide range of real-world systems, including queueing networks, Internet traffic, re-manufacturing and reverse logistics, inventory control, bio-informatics, DNA sequence analysis, genetic networks, and data mining.[reference:2][reference:3] Special attention is given to Markov decision processes for customer lifetime value (CLV) and hidden Markov models for customer classification, highlighting the book's relevance to marketing and business analytics.[reference:4]
The text is structured to be both a learning resource and a reference work. The second edition, reformatted as a textbook, further enhances its pedagogical value, making it an ideal choice for graduate-level courses and self-study.[reference:5][reference:6] The book features end-of-chapter exercises, summaries, and open problems to reinforce learning and encourage further exploration.[reference:7]
Key Features
- Comprehensive Coverage: From basic Markov chain theory to advanced multivariate and hidden Markov models, the book provides a complete treatment of the subject.[reference:8]
- Algorithmic Focus: Detailed discussion of numerical algorithms for solving Markov models, with emphasis on efficiency and practical implementation.[reference:9]
- Diverse Applications: Real-world case studies in queueing systems, Internet modeling, supply chain management, bio-informatics, and data mining.[reference:10]
- Pedagogical Design: End-of-chapter exercises, summaries, and open problems to reinforce learning and encourage further exploration.[reference:11]
- Interdisciplinary Relevance: Bridges mathematics, computer science, engineering, and business, making it useful for a wide audience.[reference:12]
- Clear Structure: Eight chapters that logically progress from fundamental concepts to cutting-edge research topics.[reference:13]
- Practical Tools: Provides models and methods directly applicable to operations research, scientific computing, and data analysis.[reference:14]
- Up-to-Date Content: Reflects recent developments in Markov chain research, including higher-order and multivariate extensions.[reference:15]
- Accessible Writing: Balances mathematical rigor with clarity, suitable for both beginners and experienced researchers.[reference:16]
- Supplementary Material: Includes additional resources and references for deeper study.[reference:17]
About Author
Wai-Ki Ching is a professor at The University of Hong Kong, with a distinguished career in applied mathematics, scientific computing, and operations research. His research interests include Markov chains, matrix theory, and optimization, with numerous publications in leading journals. He has made significant contributions to the development of Markov models for real-world applications, particularly in queueing systems and bio-informatics.[reference:18][reference:19]
Michael K. Ng is a professor at Hong Kong Baptist University and an adjunct research fellow at the E-Business Technology Institute of The University of Hong Kong.[reference:20] His expertise lies in numerical linear algebra, data mining, and machine learning, with a strong focus on algorithmic efficiency.[reference:21] Together with Prof. Ching, he has co-authored several influential works on Markov chains and their applications.
The authors' collaborative work reflects a deep synergy between theoretical mathematics and practical problem-solving, making this book a trusted resource in the academic and professional community.
Related Books
- Introduction to Probability Models - Sheldon M. Ross
- Stochastic Processes - Sheldon M. Ross
- Markov Chains and Stochastic Stability - Sean Meyn, Richard L. Tweedie
- Hidden Markov Models for Time Series: An Introduction Using R - Walter Zucchini, Iain L. MacDonald, Roland Langrock
- Applied Stochastic Processes - Ming Liao
- Queueing Systems, Volume 1: Theory - Leonard Kleinrock
- Data Mining and Analysis: Fundamental Concepts and Algorithms - Mohammed J. Zaki, Wagner Meira Jr.
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Frequently Asked Questions
Q: What is the main focus of this book?
A: The book focuses on Markov chain models, their theoretical foundations, efficient numerical algorithms, and a wide range of practical applications in fields such as queueing theory, bio-informatics, supply chain management, and data mining.[reference:22]
Q: What level of mathematical background is required?
A: A basic understanding of probability theory and linear algebra is recommended. The book is suitable for graduate students, researchers, and professionals in applied mathematics and related disciplines.[reference:23]
Q: Does the book include exercises?
A: Yes, the second edition has been reformatted as a textbook and includes end-of-chapter exercises, summaries, and open problems to facilitate learning.[reference:24]
Q: What are some of the key application areas covered?
A: The book covers queueing systems, Internet traffic modeling, re-manufacturing and reverse logistics, inventory control, bio-informatics, DNA sequence analysis, genetic networks, data mining, and customer lifetime value analysis.[reference:25][reference:26]
Q: Is this book suitable for self-study?
A: Absolutely. The clear structure, progressive difficulty, and included exercises make it an excellent resource for independent learners as well as for use in a classroom setting.[reference:27]
Q: Does the book cover both discrete-time and continuous-time Markov chains?
A: Yes, it provides an introduction to both discrete-time and continuous-time Markov chains, and later chapters build on these foundations.[reference:28]
Q: What makes this book different from other Markov chain texts?
A: It offers a balanced blend of theory, algorithms, and applications, with a strong emphasis on numerical methods and recent developments such as higher-order and multivariate models.[reference:29]
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