Title | Lectures on Probability Theory and Statistics [electronic resource] : Ecole d'Etรฉ de Probabilitรฉs de Saint-Flour XXX - 2000 / edited by Sergio Albeverio, Walter Schachermayer, Michel Talagrand, Pierre Bernard |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |
Connect to | http://dx.doi.org/10.1007/3-540-44922-1 |
Descript | X, 298 p. online resource |
Sergio 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