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Lectures on Probability Theory and Statistics

Ecole d’Eté de Probabilités de Saint-Flour XXX - 2000

  • Sergio Albeverio
  • Walter Schachermayer
  • Michel Talagrand
  • Pierre Bernard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1816)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Sergio Albeverio: Theory of Dirichlet forms and applications

  3. Walter Schachermayer: Introduction to the Mathematics of Financial Markets

  4. Michel Talagrand: Mean field models for spin glasses: a first course

  5. Back Matter
    Pages 284-296

About this book

Introduction

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.

Keywords

Dirichlet forms Loop spaces Mathematical Finance Potential Probability space Probability theory Spin glasses Statistical physics

Editors and affiliations

  • Sergio Albeverio
    • 1
  • Walter Schachermayer
    • 2
  • Michel Talagrand
    • 3
  • Pierre Bernard
    • 4
  1. 1.Institute for Applied Mathematics, Probability Theory and StatisticsUniversity of BonnBonnGermany
  2. 2.Department of Financial and Actuarial MathematicsVienna University of TechnologyViennaAustria
  3. 3.Equipe d’AnalyseUniversité Paris VIParis Cedex 05France
  4. 4.Laboratoire de Mathématiques Appliquées UMR CNRS 6620Université Blaise PascalAubière CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-44922-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40335-7
  • Online ISBN 978-3-540-44922-5
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site