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

ISBN: 9781139180795 出版年：2011 页码：814 Kobayashi Mark Turin Cambridge University Press

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.