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Lectures on Probability Theory and Statistics 2003rd ed.(Lecture Notes in Mathematics Vol.1816) P 304 p. 03

Albeverio, Sergio, Schachermayer, Walter 　著

Bernard, Pierre 　編

在庫状況海外在庫有り	お届け予定日 1ヶ月
価格 \13,712（税込）

発行年月	2003年07月
出版社／提供元	Springer-Verlag GmbH
出版国	ドイツ
言語	英語
媒体	冊子
装丁	paper
ページ数／巻数	X, 298 p.
ジャンル	洋書／理工学／数学／確率
ISBN	9783540403357
商品コード	0204051402
本の性格	学術書
新刊案内掲載月	2003年10月
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0204051402

内容

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.

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.