Probability, Random Processes, and Statistical Analysis
Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance

Covers the fundamental topics together with advanced theories, including the EM algorithm, hidden Markov models, and queueing and loss systems.

Hisashi Kobayashi (Author), Brian L. Mark (Author), William Turin (Author)

9780521895446, Cambridge University Press

Hardback, published 15 December 2011

812 pages, 114 b/w illus. 11 tables 458 exercises
25.3 x 17.8 x 4 cm, 1.7 kg

'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

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 Itô 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.

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.

Subject Areas: Signal processing [UYS], Communications engineering / telecommunications [TJK], Electronics & communications engineering [TJ], Probability & statistics [PBT], Mathematics [PB]