Titlebook: Discrete Stochastic Processes and Applications; Jean-François Collet Textbook 2018 Springer International Publishing AG, part of Springer

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Linear algebra and search engines chains on finite spaces. It is probably fair to say that the key property of the matrices (apart from being stochastic matrices) is positivity; this is why in order to make the presentation self-contained, most classical results on the Perron–Frobenius theory are included. The last section deals wi

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The Poisson processly the best (for pedagogical purposes) prototype of continuous-time Markov process, it provides a good occasion to gently introduce the concepts specific to this framework (such as right constancy, jump times, jump chain, properties of increments) before hitting the reader with the general theory, w

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Prelude: a user’s guide to convexityd applications to information theory. In particular, a certain number of classical convexity inequalities (such as Jensen’s and Young’s inequalities) are presented in a unified framework thanks to the use of Bregman’s divergences.

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Application: binary codinging, we present the fundamental inequalities of Kraft and McMillan, and then in Theorem . we present the entropic bound for the length of uniquely decipherable codes. We only touch upon the aspects of coding that have to do with entropy; a more comprehensive presentation of coding theory may be foun

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Textbook 2018 applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The fi

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0172-5939 ed introductory course to probability and information theory.This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine d

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Embryology and Congenital Anomaliesis why in order to make the presentation self-contained, most classical results on the Perron–Frobenius theory are included. The last section deals with the by now classical PageRank algorithm, which is included here because it is traditional to present it in the language of linear algebra rather than that of Markov processes.

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