LEADER 01219nas2-2200385---450- 001 990003652510203316 005 20120418093224.0 035 $a000362598 035 $aUSA01000362598 035 $a(ALEPH)000365251USA01 035 $a000362598 100 $a20120418d1969----km-y0itay50------ba 101 $arus$cheb 102 $aRU 105 $ay|||||||001yy 200 1 $aTev'e-Molocnik$aPovesti i rasskazy$f?olom-Alejhem 210 $aMoskva$cHudo?estvennaja literatura$d1969 215 $a686 p.$d20 cm 225 2 $aBiblioteka vsemirnoj literatury$v197 300 $aAutore e titoli delle opere in russo, traslitterati 410 0$1001000362594$aBiblioteka vsemirnoj literatury$v, 197$12001 454 0$12001$aTevye der milkhiker$953890 606 0 $2BNCF 676 $a839.0933$v22 700 1$aALEICHEM,$bShalom$0612128 801 0$aIT$bsalbc$gISBD 912 $a990003652510203316 951 $aVIII.1. Coll. 4/ 78$b7015 L.M.$cVIII.1. Coll.$d00309595 959 $aBK 969 $aUMA 979 $aCHIARA$b90$c20120418$lUSA01$h0931 979 $aCHIARA$b90$c20120418$lUSA01$h0932 979 $aCHIARA$b90$c20120418$lUSA01$h0932 996 $aTevye der milkhiker$953890 997 $aUNISA LEADER 05857nam 22008895 450 001 9910299974403321 005 20200705161932.0 010 $a1-4471-5361-8 024 7 $a10.1007/978-1-4471-5361-0 035 $a(CKB)3710000000078526 035 $a(Springer)9781447153610 035 $a(MH)013879479-0 035 $a(SSID)ssj0000988251 035 $a(PQKBManifestationID)11583334 035 $a(PQKBTitleCode)TC0000988251 035 $a(PQKBWorkID)10952215 035 $a(PQKB)11038098 035 $a(DE-He213)978-1-4471-5361-0 035 $a(MiAaPQ)EBC6315095 035 $a(MiAaPQ)EBC1394842 035 $a(Au-PeEL)EBL1394842 035 $a(CaPaEBR)ebr10983438 035 $a(OCoLC)870244268 035 $a(PPN)172418097 035 $a(EXLCZ)993710000000078526 100 $a20130829d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability Theory $eA Comprehensive Course /$fby Achim Klenke 205 $a2nd ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (XII, 638 p. 46 illus., 20 illus. in color.)$conline resource 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4471-5360-X 327 $aBasic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon?Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The It?o Integral -- Stochastic Differential Equations. 330 $aThis second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: ? limit theorems for sums of random variables ? martingales ? percolation ? Markov chains and electrical networks ? construction of stochastic processes ? Poisson point process and infinite divisibility ? large deviation principles and statistical physics ? Brownian motion ? stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aMeasure theory 606 $aDynamics 606 $aErgodic theory 606 $aFunctional analysis 606 $aStatistical physics 606 $aDynamics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aProbabilities. 615 0$aMeasure theory. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aFunctional analysis. 615 0$aStatistical physics. 615 0$aDynamics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aMeasure and Integration. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aFunctional Analysis. 615 24$aComplex Systems. 615 24$aStatistical Physics and Dynamical Systems. 676 $a519.2 700 $aKlenke$b Achim$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478404 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299974403321 996 $aProbability theory$9264282 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress