Stochastic Processes

Gallager, Robert G.
Robert G. Gallager is a Professor Emeritus at the Massachusetts Institute of Technology and one of the world's leading information theorists. He is a Fellow of the US National Academy of Engineering, the US National Academy of Sciences, and his numerous awards and honours include the IEEE Medal of Honour (1990) and the Marconi Prize (2003). He was awarded the MIT Graduate Student Teaching Award in 1993, and this book is based on his 20 years of experience of teaching this subject to students.

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.

The definitive textbook on stochastic processes, written by one of the world's leading information theorists, covering both theory and applications.

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.