Probability, Random Processes, and Statistical Analysis

Hisashi Kobayashi is the Sherman Fairchild University Professor Emeritus at Princeton University, where he was previously Dean of the School of Engineering and Applied Science. He also spent 15 years at the IBM Research Center, Yorktown Heights, NY, and was the Founding Director of the IBM Tokyo Research Laboratory. He is an IEEE Life Fellow, an IEICE Fellow, was elected to the Engineering Academy of Japan (1992) and received the 2005 Eduard Rhein Technology Award. Brian L. Mark is a Professor in the Department of Electrical and Computer Engineering at George Mason University. Prior to this, he was a Research Staff Member at the NEC C&C Research Laboratories in Princeton, New Jersey and in 2002 he received a National Science Foundation CAREER award. William Turin is currently a Consultant at AT&T Labs Research. As a Member of Technical Staff at AT&T Bell Laboratories and later a Technology Consultant at AT&T Labs Research for 21 years, he developed methods for qualifying the performance of communication systems. He is the author of six books and numerous papers.

'This book provides a very comprehensive, well-written and modern approach to the fundamentals of probability and random processes, together with their applications in the statistical analysis of data and signals. … It provides a one-stop, unified treatment that gives the reader an understanding of the models, methodologies and underlying principles behind many of the most important statistical problems arising in engineering and the sciences today.' Dean H. Vincent Poor, Princeton University

• 1. Introduction; Part I. Probability, Random Variables and Statistics: 2. Probability; 3. Discrete random variables; 4. Continuous random variables; 5. Functions of random variables and their distributions; 6. Fundamentals of statistical analysis; 7. Distributions derived from the normal distribution; Part II. Transform Methods, Bounds and Limits: 8. Moment generating function and characteristic function; 9. Generating function and Laplace transform; 10. Inequalities, bounds and large deviation approximation; 11. Convergence of a sequence of random variables, and the limit theorems; Part III. Random Processes: 12. Random process; 13. Spectral representation of random processes and time series; 14. Poisson process, birth-death process, and renewal process; 15. Discrete-time Markov chains; 16. Semi-Markov processes and continuous-time Markov chains; 17. Random walk, Brownian motion, diffusion and itô processes; Part IV. Statistical Inference: 18. Estimation and decision theory; 19. Estimation algorithms; Part V. Applications and Advanced Topics: 20. Hidden Markov models and applications; 21. Probabilistic models in machine learning; 22. Filtering and prediction of random processes; 23. Queuing and loss models.