LEADER 04761nam 22006735 450 001 9910144601803321 005 20201106135937.0 010 $a3-540-44922-1 024 7 $a10.1007/3-540-44922-1 035 $a(CKB)1000000000233100 035 $a(SSID)ssj0000324383 035 $a(PQKBManifestationID)11236843 035 $a(PQKBTitleCode)TC0000324383 035 $a(PQKBWorkID)10313072 035 $a(PQKB)10747860 035 $a(DE-He213)978-3-540-44922-5 035 $a(MiAaPQ)EBC3072350 035 $a(PPN)15519089X 035 $a(EXLCZ)991000000000233100 100 $a20121227d2003 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Probability Theory and Statistics $eEcole d'Eté de Probabilités de Saint-Flour XXX - 2000 /$fby Sergio Albeverio, Walter Schachermayer ; edited by Pierre Bernard 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (X, 298 p.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1816 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-40335-3 320 $aIncludes bibliographical references. 327 $aSergio Albeverio: Theory of Dirichlet forms and applications -- Functional analytic background: semigroups, generators, resolvents -- Closed symmetric coercive forms associated with Co-contraction semigroups -- Contraction properties of forms, positivity preserving and submarkovian semigroups -- Potential Theory and Markov Processes associated with Dirichlet Forms -- Diffusions and stochastic differential equations associated with classical Dirichlet forms -- Applications -- Walter Schachermayer: Introduction to the Mathematics of Financial Markets -- Introduction: Bachelier?s Thesis from 1900 -- Models of Financial Markets on Finite Probability Spaces -- The Binomial Model, Bachelier?s Model and the Black-Scholes Model -- The No-Arbitrage Theory for General Processes -- Some Applications of the Fundamental Theorem of Asset Pricing -- Michel Talagrand: Mean field models for spin glasses: a first course -- What this is all about: the REM -- The Sherrington-Kirkpatrick model at high temperature -- The p-spin interaction model -- External field and the replica-symmetric solution -- Exponential inequalities -- Central limit theorems and the Almeida-Thouless line -- Emergence and separation of the lumps in the p-spin interaction model. 330 $aIn World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1816 606 $aProbabilities 606 $aMathematical physics 606 $aEconomics, Mathematical  606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062 615 0$aProbabilities. 615 0$aMathematical physics. 615 0$aEconomics, Mathematical . 615 14$aProbability Theory and Stochastic Processes. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aQuantitative Finance. 676 $a576.58 700 $aAlbeverio$b Sergio$4aut$4http://id.loc.gov/vocabulary/relators/aut$044256 702 $aSchachermayer$b Walter$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aBernard$b Pierre$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144601803321 996 $aLectures on Probability Theory and Statistics$92514973 997 $aUNINA