Discrete Stochastic Processes and Applications (Universitext)
Provides applications to Markov processes, coding/informationtheory, population dynamics, and search engine designIdeal for a newly designed introductory course to probabilityand information theoryPresents an engaging treatment of entropyReader develops solid probabilistic intuition without the needfor a course in measure theory——————————This unique text for beginning graduate students gives aself-contained introduction to the mathematical properties ofstochastics and presents their applications to Markov processes,coding theory, population dynamics, and search engine design. Thebook is ideal for a newly designed course in an introduction toprobability and information theory. Prerequisites include workingknowledge of linear algebra, calculus, and probability theory. Thefirst part of the text focuses on the rigorous theory of Markovprocesses on countable spaces (Markov chains) and provides thebasis to developing solid probabilistic intuition without the needfor a course in measure theory. The approach taken is gradualbeginning with the case of discrete time and moving on to that ofcontinuous time. The second part of this text is more applied; itscore introduces various uses of convexity in probability andpresents a nice treatment of entropy.