"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 applicationsof 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 20 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"--

"Basic underlying principles and axioms are made clear from the start, and new topics are developed as needed, encouraging and enabling students to develop an instinctive grasp of the fundamentals. Mathematical proofs are made easy for students to understand and remember, helping them quickly learn how to choose and apply the best possible models to real-world situations"--

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