This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study.
After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth–death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter.
Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.
Dr. Robert C. Creese, Certified Cost Engineer (CCE), is Professor of Industrial and Management Systems Engineering at West Virginia University, USA and recently has taught courses on Engineering Economy, Advanced Engineering Economics, Cost and Estimating for Manufacturing, Manufacturing Processes and Advanced Manufacturing Processes. He has previously taught at The Pennsylvania State University (9 years), Grove City College (4 years), Aalborg University in Denmark (3 sabbaticals) and at West Virginia University for over 31 years. He is a Fellow of the Association for the Advancement of Cost Engineering, International (AACEI), received the Charles V. Keane Service Award and Brian D. Dunfield Educational Service Award presented by AACE, and has been treasurer of the Northern West Virginia Section of AACE for more than 20 years. He is a Life Member of AACE International, ASEE (American Society for Engineering Education) and ASM (American Society for Materials). He also is a member of ISPA, SCEA, AIST, AWS, and AFS. He obtained his B.S. Degree in Industrial Engineering from the Pennsylvania State University, his M.S. Degree in Industrial Engineering from the University of California at Berkeley, and his Ph.D. Degree in Metallurgy from the Pennsylvania State University. He has authored the book Introduction to Manufacturing Processes and Materials (Marcel Dekker, 1999) and co-authored two books Estimating and Costing for the Metal Manufacturing Industries (Marcel Dekker, 1992) with Dr. M. Adithan of VIT University Vellore, India and Dr. B. S. Pabla of the Technical Teachers' Training Institute, Chandigarh, India and Strategic Cost Analysis for Project Managers and Engineers (New Age International Publishers, 2010) with Dr. M. Adithan, VIT University, Vellore, India. He has authored and co-authored more than 100 technical papers.
