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Nonstandard Methods In Stochastic Analysis And Mathematical Physics


Nonstandard Methods In Stochastic Analysis And Mathematical Physics
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Nonstandard Methods In Stochastic Analysis And Mathematical Physics


Nonstandard Methods In Stochastic Analysis And Mathematical Physics
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Author : Sergio Albeverio
language : en
Publisher: Courier Dover Publications
Release Date : 2009-02-26

Nonstandard Methods In Stochastic Analysis And Mathematical Physics written by Sergio Albeverio and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-26 with Mathematics categories.


Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.



Nonstandard Methods In Stochastic Analysis And Mathematical Physics


Nonstandard Methods In Stochastic Analysis And Mathematical Physics
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Author : Sergio Albeverio
language : en
Publisher:
Release Date : 1986

Nonstandard Methods In Stochastic Analysis And Mathematical Physics written by Sergio Albeverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.




Nonstandard Analysis


Nonstandard Analysis
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Author : Leif O. Arkeryd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonstandard Analysis written by Leif O. Arkeryd 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 2012-12-06 with Mathematics categories.


1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.



Nonstandard Analysis For The Working Mathematician


Nonstandard Analysis For The Working Mathematician
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Author : Peter A. Loeb
language : en
Publisher: Springer
Release Date : 2015-08-26

Nonstandard Analysis For The Working Mathematician written by Peter A. Loeb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-26 with Mathematics categories.


Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.



Non Standard Analysis


Non Standard Analysis
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Author : Abraham Robinson
language : en
Publisher: Princeton University Press
Release Date : 2016-08-11

Non Standard Analysis written by Abraham Robinson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-11 with Mathematics categories.


Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.



Nonstandard Methods In The Calculus Of Variations


Nonstandard Methods In The Calculus Of Variations
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Author : Curtis Tuckey
language : en
Publisher: CRC Press
Release Date : 1993-11-22

Nonstandard Methods In The Calculus Of Variations written by Curtis Tuckey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-22 with Mathematics categories.


This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.



Quantum And Stochastic Mathematical Physics


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.



Seminar On Stochastic Analysis Random Fields And Applications Iii


Seminar On Stochastic Analysis Random Fields And Applications Iii
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Author : Robert C. Dalang
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Seminar On Stochastic Analysis Random Fields And Applications Iii written by Robert C. Dalang and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.



Nonstandard Analysis


Nonstandard Analysis
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Author : Leif O. Arkeryd
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-30

Nonstandard Analysis written by Leif O. Arkeryd 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 1997-04-30 with Mathematics categories.


1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.



Nonstandard Analysis


Nonstandard Analysis
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Author : Martin Väth
language : en
Publisher: Springer Science & Business Media
Release Date : 2007

Nonstandard Analysis written by Martin Väth 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 2007 with Mathematics categories.


This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.