Loeb Measures In Practice

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Loeb Measures In Practice Recent Advances

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Author : Nigel Cutland
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-12-12

Loeb Measures In Practice Recent Advances written by Nigel Cutland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-12 with Business & Economics categories.

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.

Loeb Measures In Practice

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Author : Nigel J. Cutland
language : en
Publisher:
Release Date : 2014-01-15

Loeb Measures In Practice written by Nigel J. Cutland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

How To Measure The Infinite Mathematics With Infinite And Infinitesimal Numbers

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Author : Vieri Benci
language : en
Publisher: World Scientific
Release Date : 2019-02-19

How To Measure The Infinite Mathematics With Infinite And Infinitesimal Numbers written by Vieri Benci and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-19 with Mathematics categories.

'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.

Beyond First Order Model Theory Volume I

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Author : Jose Iovino
language : en
Publisher: CRC Press
Release Date : 2017-08-14

Beyond First Order Model Theory Volume I written by Jose Iovino and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.

Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.

Probabilistic Methods In Fluids Proceedings Of The Swansea 2002 Workshop

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Author : Ian M Davies
language : en
Publisher: World Scientific
Release Date : 2003-06-13

Probabilistic Methods In Fluids Proceedings Of The Swansea 2002 Workshop written by Ian M Davies and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-13 with Mathematics categories.

This volume contains recent research papers presented at the international workshop on “Probabilistic Methods in Fluids” held in Swansea. The central problems considered were turbulence and the Navier-Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.

Quantum And Stochastic Mathematical Physics

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Author : Astrid Hilbert
language : en
Publisher: Springer Nature
Release Date : 2023-04-02

Quantum And Stochastic Mathematical Physics written by Astrid Hilbert and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-02 with Mathematics categories.

Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.

Nonstandard Analysis Axiomatically

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Author : Vladimir Kanovei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Nonstandard Analysis Axiomatically written by Vladimir Kanovei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

Mathematical Theory Of Nonequilibrium Steady States

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Author : Da-Quan Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Mathematical Theory Of Nonequilibrium Steady States written by Da-Quan Jiang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Markov processes categories.

Pointwise Convergence Of Fourier Series

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Author : Juan Arias de Reyna
language : en
Publisher: Springer
Release Date : 2004-10-13

Pointwise Convergence Of Fourier Series written by Juan Arias de Reyna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-13 with Mathematics categories.

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

Calculus Of Variations And Nonlinear Partial Differential Equations

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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02

Calculus Of Variations And Nonlinear Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-02 with Mathematics categories.

With a historical overview by Elvira Mascolo