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Author:   Imme van den Berg ,  Vitor Neves
Publisher:   Springer Verlag GmbH
Imprint:   Springer Verlag GmbH
Edition:   2007 ed.
Dimensions:   Width: 17.00cm , Height: 2.30cm , Length: 24.20cm
Weight:   0.930kg
ISBN:  

9783211499047

ISBN 10:   3211499040
Pages:   401
Publication Date:   27 December 2006
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Foundations.- The strength of nonstandard analysis.- The virtue of simplicity.- Analysis of various practices of referring in classical or non standard mathematics.- Stratified analysis?.- ERNA at work.- The Sousa Pinto approach to nonstandard generalised functions.- Neutrices in more dimensions.- Number theory.- Nonstandard methods for additive and combinatorial number theory. A survey.- Nonstandard methods and the Erd?s-Turán conjecture.- Statistics, probability and measures.- Nonstandard likelihood ratio test in exponential families.- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup.- On two recent applications of nonstandard analysis to the theory of financial markets.- Quantum Bernoulli experiments and quantum stochastic processes.- Applications of rich measure spaces formed from nonstandard models.- More on S-measures.- A Radon-Nikodým theorem for a vector-valued reference measure.- Differentiability of Loeb measures.- Differential systems and equations.- The power of Gâteaux differentiability.- Nonstandard Palais-Smale conditions.- Averaging for ordinary differential equations and functional differential equations.- Path-space measure for stochastic differential equation with a coefficient of polynomial growth.- Optimal control for Navier-Stokes equations.- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations.- Infinitesimals and education.- Calculus with infinitesimals.- Pre-University Analysis.

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