Probability, Random Processes, and Statistical Analysis : Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Ito process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum-Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
- Electronic book text
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 114 b/w illus. 11 tables 458 exercises
'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 'This is a well-written up-to-date graduate text on probabilty and random processes. It is unique in combining statistical analysis with the probabilistic material. As noted by the authors, the material, as presented, can be used in a variety of current application areas, ranging from communications to bioinformatics. I particularly liked the historical introduction, which should make the field exciting to the student, as well as the introductory chapter on probability, which clearly describes for the student the distinction between the relative frequency and axiomatic approaches to probability. I recommend it unhesitatingly. It deserves to become a leading text in the field.' Professor Emeritus Mischa Schwartz, Columbia University 'Hisashi Kobayashi, Brian L. Mark, and William Turin are highly experienced university teachers and scientists. Based on this background their book covers not only fundamentals but also a large range of applications. Some of them are treated in a textbook for the first time. ... Without any doubt the book will be extremely valuable to graduate students and to scientists in universities and industry as well. Congratulations to the authors!' Prof. Dr.-Ing. Eberhard Hansler, Technische Universitat Darmstadt 'An up-to-date and comprehensive book with all the fundamentals in Probability, Random Processes, Stochastic Analysis, and their interplays and applications, which lays a solid foundation for the students in related areas. It is also an ideal textbook with five relatively independent but logically interconnected parts and the corresponding solution manuals and lecture slides. Furthermore, to my best knowledge, the similar editing in Part IV and Part V can't be found elsewhere.' Zhisheng Niu, Tsinghua University
Table of contents
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 ito 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.