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

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書目名稱Discrete Stochastic Processes and Applications
編輯Jean-Fran?ois Collet
視頻videohttp://file.papertrans.cn/282/281165/281165.mp4
概述Provides applications to Markov processes, coding/information theory, population dynamics, and search engine design.Ideal for a newly designed introductory course to probability and information theory
叢書名稱Universitext
圖書封面Titlebook: Discrete Stochastic Processes and Applications;  Jean-Fran?ois Collet Textbook 2018 Springer International Publishing AG, part of Springer
描述.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 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 first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy..
出版日期Textbook 2018
關(guān)鍵詞Markov processes; Brownian motion; Perron-Frobenius theorem; Poisson process; information theory; search
版次1
doihttps://doi.org/10.1007/978-3-319-74018-8
isbn_softcover978-3-319-74017-1
isbn_ebook978-3-319-74018-8Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer International Publishing AG, part of Springer Nature 2018
The information of publication is updating

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Jean-Fran?ois Bach,Mireille Dardenne by formalizing the idea of lack of memory, which will be made rigorous in the definition of Markov processes. The use of the law of total probability will lead to the definition of the transition matrix, which encodes the dynamics of .. The problem is then to extract from this transition matrix inf
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Robert ?migielski,Bertram Zarinsd 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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Robert ?migielski,Bertram Zarinsing, 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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