Markov processes are used to model systems with limited memory. They are used in many areas including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queuing systems, resource management, dams, financial engineering, actuarial science, and decision systems. This book, which is written for upper level undergraduate and graduate students, and researchers, presents a unified presentation of Markov processes.In addition to traditional topics such as Markovian queuing system, the book discusses such topics as continuous-time random walk, correlated random walk, Brownian motion, diffusion processes, hidden Markov models, Markov random fields, Markov point processes and Markov chain Monte Carlo. Continuous-time random walk is currently used in econophysics to model the financial market, which has traditionally been modeled as a Brownian motion.Correlated random walk is popularly used in ecological studies to model animal and insect movement. Hidden Markov models are used in speech analysis and DNA sequence analysis while Markov random fields and Markov point processes are used in image analysis. Thus, the book is designed to have a very broad appeal. It provides the practical, current applications of Markov processes, and covers HMM, Point processes, and Monte Carlo. It includes enough theory to help students gain thorough understanding of the subject. Principles can be immediately applied in many specific research projects, saving researchers time. The end of chapter exercises provide reinforcement, practice and increased understanding to the student.
1 Basic Concepts 1
2 Introduction to Markov Processes 45
3 Discrete-Time Markov Chains 55
4 Continuous-Time Markov Chains 83
5 Markovian Queueing Systems 105
6 Markov Renewal Processes 153
7 Markovian Arrival Processes 185
8 Random Walk 215
9 Brownian Motion and Diffusion Processes 263
10 Controlled Markov Processes 297
11 Hidden Markov Models 341
12 Markov Random Fields 381
13 Markov Point Processes 401
14 Markov Chain Monte Carlo 423
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