Lectures on Probability Theory and Statistics: Ecole d’Eté de Probabilités de Saint-Flour XXX - 2000

Functional analytic background: semigroups, generators, resolvents....Pages 7-17
Closed symmetric coercive forms associated with C o -contraction semigroups....Pages 18-32
Contraction properties of forms, positivity preserving and submarkovian semigroups....Pages 33-43
Potential Theory and Markov Processes associated with Dirichlet Forms....Pages 43-51
Diffusions and stochastic differential equations associated with classical Dirichlet forms....Pages 51-63
Applications....Pages 64-73
Introduction: Bachelier’s Thesis from 1900....Pages 111-126
Models of Financial Markets on Finite Probability Spaces....Pages 127-139
The Binomial Model, Bachelier’s Model and the Black-Scholes Model....Pages 140-152
The No-Arbitrage Theory for General Processes....Pages 153-172
Some Applications of the Fundamental Theorem of Asset Pricing....Pages 173-179
Introduction....Pages 185-187
What this is all about: the REM....Pages 188-200
The Sherrington-Kirkpatrick model at high temperature....Pages 201-212
The p -spin interaction model....Pages 213-220
External field and the replica-symmetric solution....Pages 221-239
Exponential inequalities....Pages 240-252
Central limit theorems and the Almeida-Thouless line....Pages 253-268
Emergence and separation of the lumps in the p -spin interaction model....Pages 269-283