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

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, queueing and loss networks, and 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.

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.