Overview
- New edition now focused on applications where Markov chains have seen explosive growth
- New edition now with exercises in each chapter
- Three of the authors are among the leading researchers/academics in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 189)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.
This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods for solving linear systems will be introduced for finding the stationary distribution of a Markov chain. The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov decision processes (MDPs).
Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chain for computing the PageRank, the ranking of websites on the Internet. Chapter 3 studies Markovian models for manufacturing and re-manufacturing systems and presents closed form solutions and fast numerical algorithms for solving the captured systems. In Chapter 4, the authors present a simple hidden Markov model (HMM) with fast numerical algorithms for estimating the model parameters. An application of the HMM for customer classification is also presented.
Chapter 5 discusses Markov decision processes for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. The authors present an approach based on Markov decision processes for the calculation of CLV using real data.
Chapter 6 considers higher-order Markov chain models, particularly a class of parsimonious higher-order Markov chain models. Efficient estimation methods for model parameters based on linear programming are presented. Contemporary research results on applications to demand predictions, inventory control and financial risk measurement are also presented. In Chapter 7, a class of parsimonious multivariate Markov models is introduced. Again, efficient estimation methods based on linear programming are presented. Applications to demand predictions, inventory control policy and modeling credit ratings data are discussed. Finally, Chapter 8 re-visits hidden Markov models, and the authors present a new class of hidden Markov models with efficient algorithms for estimating the model parameters. Applications to modeling interest rates, credit ratings and default data are discussed.
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This book is aimed at senior undergraduate students, postgraduate students, professionals, practitioners, and researchers in applied mathematics, computational science, operational research, management science and finance, who are interested in the formulation and computation of queueing networks, Markov chain models and related topics. Readers are expected to have some basic knowledge of probability theory, Markov processes and matrix theory.
Reviews
From the reviews of the First Edition:
"The authors outline recent developments of Markov chain models … . This book is aimed at students, professionals, practitioners, and researchers in scientific computing and operational research, who are interested in the formulation and computation of queuing and manufacturing systems. It gives a number of useful tools for researchers in real applications … ." (Alexander I. Zejfman, Zentralblatt MATH, Vol. 1089 (15), 2006)
"In this book’s … essential notions on Markov chains, hidden Markov models, and Markov decision processes are covered, with special emphasis on iterative methods for solving linear systems. … Each chapter finishes with a short summary and sometimes a selection of open problems. … This book is intended for students and researchers in applied mathematics, scientific computing, and operations research … . Overall, this book offers much interesting and up-to-date material on a wide variety of topics, dealing with finite-space Markov processes." (Jozef L. Teugels, Journal of the American Statistical Association, Vol. 103 (483), September, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Markov Chains
Book Subtitle: Models, Algorithms and Applications
Authors: Wai-Ki Ching, Ximin Huang, Michael K. Ng, Tak-Kuen Siu
Series Title: International Series in Operations Research & Management Science
DOI: https://doi.org/10.1007/978-1-4614-6312-2
Publisher: Springer New York, NY
eBook Packages: Business and Economics, Business and Management (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-6311-5Published: 28 March 2013
Softcover ISBN: 978-1-4899-9752-4Published: 05 April 2015
eBook ISBN: 978-1-4614-6312-2Published: 27 March 2013
Series ISSN: 0884-8289
Series E-ISSN: 2214-7934
Edition Number: 2
Number of Pages: XVI, 243
Topics: Operations Research/Decision Theory, Operations Research, Management Science, Probability Theory and Stochastic Processes