Ebook: Lectures on Probability Theory and Statistics: Ecole d’Eté de Probabilités de Saint-Flour XXX - 2000
- Tags: Probability Theory and Stochastic Processes, Mathematical and Computational Physics, Quantitative Finance
- Series: Lecture Notes in Mathematics 1816
- Year: 2003
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English-French
- pdf
In 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.
In 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.
In 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.
Content:
Front Matter....Pages I-VIII
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
Back Matter....Pages 284-296
In 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.
Content:
Front Matter....Pages I-VIII
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
Back Matter....Pages 284-296
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