The definitive textbook on stochastic processes, written by one of the world's leading information theorists, covering both theory and applications.
This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.
1. Introduction and review of probability; 2. Poisson processes; 3. Gaussian random vectors and processes; 4. Finite-state Markov chains; 5. Renewal processes; 6. Countable-state Markov chains; 7. Markov processes with countable state spaces; 8. Detection, decisions, and hypothesis testing; 9. Random walks, large deviations, and martingales; 10. Estimation.