03212nam 22005175 450 991030012330332120200630150759.03-319-74018-010.1007/978-3-319-74018-8(CKB)4100000003359310(DE-He213)978-3-319-74018-8(MiAaPQ)EBC6312150(MiAaPQ)EBC5577678(Au-PeEL)EBL5577678(OCoLC)1030992186(PPN)226693147(EXLCZ)99410000000335931020180405d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierDiscrete Stochastic Processes and Applications /by Jean-François Collet1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XVII, 220 p. 3 illus.) Universitext,0172-59393-319-74017-2 Includes bibliographical references and index.Preface -- I. Markov processes -- 1. Discrete time, countable space -- 2. Linear algebra and search engines -- 3. The Poisson process -- 4. Continuous time, discrete space -- 5. Examples -- II. Entropy and applications -- 6. Prelude: a user's guide to convexity -- 7. The basic quantities of information theory -- 8. An example of application: binary coding -- A. Some useful facts from calculus -- B. Some useful facts from probability -- C. Some useful facts from linear algebra -- D. An arithmetical lemma -- E. Table of exponential families -- References -- Index.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.Universitext,0172-5939ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.519.2Collet Jean-Françoisauthttp://id.loc.gov/vocabulary/relators/aut768230MiAaPQMiAaPQMiAaPQBOOK9910300123303321Discrete Stochastic Processes and Applications1564706UNINA