Gallager R.G. Stochastic Processes: Theory for Applications

Cambridge University Press, 2014. — 560 p. — ISBN: 1107039754, 9781107039759This 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 modeling 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.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.Introduction and review of probability
Poisson processes
Gaussian random vectors and processes
Finite-state Markov chains
Renewal processes
Countable-state Markov chains
Markov processes with countable state spaces
Detection, decisions, and hypothesis testing
Random walks, large deviations, and martingales
Estimation.