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050 4 _aQA274-274.9
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072 7 _aMAT029000
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082 0 4 _a519.2
_223
245 1 0 _aLectures on Probability Theory and Statistics
_h[electronic resource] :
_bEcole d’Eté de Probabilités de Saint-Flour XXX - 2000 /
_cedited by Sergio Albeverio, Walter Schachermayer, Michel Talagrand, Pierre Bernard.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2003.
300 _aX, 298 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
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_2rdacarrier
347 _atext file
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490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1816
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aFinance.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aQuantitative Finance.
_0http://scigraph.springernature.com/things/product-market-codes/M13062
700 1 _aAlbeverio, Sergio.
_eeditor.
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700 1 _aSchachermayer, Walter.
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700 1 _aTalagrand, Michel.
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700 1 _aBernard, Pierre.
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710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540403357
776 0 8 _iPrinted edition:
_z9783662174463
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1816
856 4 0 _uhttps://doi.org/10.1007/3-540-44922-1
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