 | Information Theory by Robert B. Ash
Buy new: $10.85 / Used from: $4.98 An excellent book on the mathematical basis of information theory. Is a good reference to the ones who enjoy the descriptions based on random processes.
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 | Adventures in Stochastic Processes by Sidney I. Resnick
Buy used from: $54.99 It is a good book if you want it as a bridge between basic processes and the advance ones. It is at the level of engineering so some formal facts are omitted.
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 | Probability and Measure, 3rd Edition by Patrick Billingsley
Buy new: $108.00 / Used from: $69.99 It is a classic but I don't like it very much. The definitions are sometimes redundant and repetitive. The best part is the proof of the strong law of large numbers it gives
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 | Introduction to the Theory of Random Processes (Dover Books on Mathematics) by Iosif I. Gikhman
Buy new: $17.90 / Used from: $8.94 This is a master piece, the chapters on measure theory and foundations of probability are one of the best I have ever seen. It then follows a rigorous description of general random processes.
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 | Entropy and Information Theory by Robert M. Gray
Buy used from: $160.99 This is one of the few books in information theory that uses measure theoretical facts and results that come from entropy theory. The explanations are sometimes confusing, but in general is a good one
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 | Applied Probability and Queues (Stochastic Modelling and Applied Probability) by Soeren Asmussen
Buy new: $63.96 / Used from: $58.94 This is a formal book on applications of probability; the notation is a little bit confusing but if you pass these is an excellent book.
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 | Stochastic Differential Equations: An Introduction with Applications (Universitext) by Bernt Oksendal
Buy new: $38.00 / Used from: $46.14 Is maybe the simplest introduction to the topic; Read it and then follow to a more advance one.
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 | Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics) by Ioannis Karatzas
Buy new: $49.80 / Used from: $41.06 This is the hard one. It is written as a formal reference, so you must take your time to give an interpretation of the topic.
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 | Stochastic Calculus and Financial Applications by J. Michael Steele
Buy new: $71.96 / Used from: $49.99 A middle point between the one by Oksendal and the one by Karatzas-Shrerve. I don't like it because is really written for specialist on business.
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 | An Introduction to Statistical Communication Theory: An IEEE Press Classic Reissue by David Middleton
Buy new: $165.00 / Used from: $86.01 An excellent book on the topic. I strongly recommend it for mathematician and physical sciences students who want to give an advance to the topic. It has developments on performance analysis.
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 | Information Theory And The Central Limit Theorem by Oliver Johnson
Buy new: $58.30 / Used from: $82.28 An interesting perspective that proves fundamental asymptotic behavior on statistics using entropy theory.
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 | Information Theory: 50 Years of Discovery
Buy new: $150.00 / Used from: $85.00 Read it so you can have an introduction to more advance a general topics including modern channel models.
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