LEADER 03212nam 22005175 450 001 9910300123303321 005 20200630150759.0 010 $a3-319-74018-0 024 7 $a10.1007/978-3-319-74018-8 035 $a(CKB)4100000003359310 035 $a(DE-He213)978-3-319-74018-8 035 $a(MiAaPQ)EBC6312150 035 $a(MiAaPQ)EBC5577678 035 $a(Au-PeEL)EBL5577678 035 $a(OCoLC)1030992186 035 $a(PPN)226693147 035 $a(EXLCZ)994100000003359310 100 $a20180405d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiscrete Stochastic Processes and Applications /$fby Jean-François Collet 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XVII, 220 p. 3 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-74017-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aCollet$b Jean-François$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768230 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300123303321 996 $aDiscrete Stochastic Processes and Applications$91564706 997 $aUNINA