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Lectures on Probability Theory and Statistics : Ecole d'Ete de Probabilites de Saint-Flour XXX - 2000 - Sergio Albeverio

Lectures on Probability Theory and Statistics

Ecole d'Ete de Probabilites de Saint-Flour XXX - 2000

Paperback Published: 14th July 2003
ISBN: 9783540403357
Number Of Pages: 298

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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.

S. Albeverio: Theory of Dirichlet forms and applications: 0. Introduction
Functional analytic background: semigroups, generators, resolvents
Closed symmetric coersive forms associated with C0-contraction semigroups
Contraction properties of forms, positivity preserving and submarkovian semigroups
Potentialnbsp;Theory and Markov Processes associated with Dirichlet Forms.-nbsp;5. Diffusions and stochastic differential equations associated with classical Dirichlet Forms
Applications 21
W. Schachermayer: Introduction to the Mathematics of Financial Markets
Introduction: Bachelier's Thesis from 1900
Models of Financial Markets on Finite Probabilitynbsp;Spaces
The Binomial Model, Bachelier's Model and the Blach-Scholes Model
The No-Arbitrage Theory for General Processes
Some Applications of the Fundamental Theorem of Asset Pricing
M. 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-Thoules line
Emergence and separation of the lumps in the p-spin interaction model
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540403357
ISBN-10: 3540403353
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English , French
Number Of Pages: 298
Published: 14th July 2003
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.65
Weight (kg): 0.44