The Resource Nonstandard Analysis : Theory and Applications, edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson, (electronic resource)

Nonstandard Analysis : Theory and Applications, edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson, (electronic resource)

Label
Nonstandard Analysis : Theory and Applications
Title
Nonstandard Analysis
Title remainder
Theory and Applications
Statement of responsibility
edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson
Title variation
Proceedings of the NATO Advanced Study Institute on Nonstandard Analysis and its Applications, International Centre for Mathematical Studies, Endinburgh, Scotland, 30 June-13 July 1996
Creator
Contributor
Subject
Genre
Language
eng
Summary
This book presents a careful and detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis. Further articles expound recent, more advanced applications in functional analysis, stochastic differential equations, mathematical physics and mathematical finance theory. All authors are world leaders in the subject. <br/> <em>Audience:</em> All mathematicians at postgraduate level and beyond who wish to learn the basics of nonstandard analysis and its role in current mathematical research
Member of
Cataloging source
I9W
http://library.link/vocab/creatorName
Arkeryd, Leif O
Dewey number
511.3
Index
no index present
LC call number
QA299.82
Literary form
non fiction
Nature of contents
encyclopedias
http://library.link/vocab/relatedWorkOrContributorName
  • Cutland, Nigel J
  • Henson, C. Ward
Series statement
NATO ASI Series, Series C: Mathematical and Physical Sciences, 1389-2185
Series volume
493
http://library.link/vocab/subjectName
  • Nonstandard mathematical analysis
  • Nonstandard mathematical analysis
Label
Nonstandard Analysis : Theory and Applications, edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson, (electronic resource)
Link
http://dx.doi.org/10.1007/978-94-011-5544-1
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Foundations of Nonstandard Analysis A Gentle Introduction to Nonstandard Extensions -- 1 Introduction -- 2 Nonstandard Extensions -- 3 Logical Formulas -- 4 Nonstandard Extensions of Multisets -- 5 Nonstandard Extensions of the Multiset (X, P(X)) -- 6 Superstructures -- 7 Saturation -- Nonstandard Real Analysis -- 1 Introduction -- 2 Basic Properties of *? -- 3 Sequences and Series -- 4 Continuity -- 5 Differentiation -- 6 Riemann Integration -- 7 Topology on ? -- 8 Using Internal Subsets of *? -- 9 An Application: Differential Equations -- Nonstandard Analysis and Topology -- 1 Metric and Topological Spaces -- 2 Continuous Mappings -- 3 Convergence -- 4 More on Topologies -- 5 Compact Spaces -- 6 Product Spaces -- 7 Restricted or Relative Topologies -- 8 Uniform Continuity on Metric Spaces -- 9 Nonstandard Hulls -- 10 Compactifications -- 11 More Exercises -- Loeb Measure and Probability -- 1 Introduction -- 2 Finite Loeb Measure -- 3 Constructing Standard Measures -- 4 Representing Standard Measures -- 5 Measurable Functions -- 6 Integration Theory -- 7 Probability Theory -- 8 Advertisement -- 9 Exercises -- An Introduction to Nonstandard Functional Analysis -- 1 Elementary Nonstandard Analysis of Normed Linear Spaces -- 2 Advanced Theory of Banach Spaces -- 3 Elementary Theory of Linear Operators -- 4 Spectral Theory of Bounded Operators -- 5 Applications of Nonstandard Spectral Theory -- 6 Closed Operators -- Applications of Nonstandard Analysis in Ordinary Differential Equations -- 1 Introduction -- 2 Tools in NSA -- 3 Differential Equations and Recursive Sequences -- 4 Regular Perturbations -- 5 Example -- 6 Dynamical Systems: Notions of Stability -- 7 Singular Perturbations -- Better Nonstandard Universes with Applications -- 1 Introduction -- 2 The Isomorphism Property -- 3 The Special Model Axiom and Full Saturation -- 4 The ?-Bolzano-Weierstrass Property -- Internal Martingales and Stochastic Integration -- 1 Hyperfinite Probability Spaces -- 2 Poisson Processes -- 3 Brownian Motion -- 4 Internal Martingales -- 5 Doob's Inequality -- 6 Quadratic Variation -- 7 Standard Parts -- 8 S-continuity -- 9 Stochastic Integration -- 10 Itô's Formula -- 11 Lévy's Characterization of Brownian Motion -- 12 Connections to Standard Theory -- 13 Stochastic Integrals in Higher Dimensions -- 14 Stochastic Differential Equations -- 15 Brownian Local Time -- 16 The Infinite Dimensional Ornstein-Uhlenbeck Process -- Stochastic Differential Equations with Extra Properties -- 1 Introduction -- 2 Spaces of Stochastic Processes -- 3 Solutions of Stochastic Differential Equations -- 4 Solutions which are Markov Processes -- 5 A Fixed Point Theorem -- 6 Stochastic Differential Equations with Nondegenerate Coefficients -- Hyperfinite Mathematical Finance -- 1 Introduction -- 2 Finite Market Models -- 3 Pricing Options in a Hyperfinite CRR Model -- 4 Hyperfinite Trading Strategies -- 5 Convergence of Prices and Strategies -- 6 Further Developments -- Applications of Nsa to Mathematical Physics -- 1 A Kinetic Inequality -- 2 The Time Asymptotic Behaviour for Certain Rarefied Gases when the Incoming Fluxes at the Boundary are Given -- 3 On Semiclassical Limits for the Schrödinger Equation -- A Nonstandard Approach to Hydromechanics Navier-Stokes Equations -- 1 Introduction -- 2 Deterministic Navier-Stokes Equations -- 3 Statistical Solutions -- 4 Stochastic Equations -- 5 Some Open Problems
Dimensions
unknown
Extent
1 online resource (384 pages).
Form of item
online
Isbn
9789401155441
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-94-011-5544-1
Specific material designation
remote
System control number
  • (OCoLC)840311313
  • (OCoLC)ocn840311313
Label
Nonstandard Analysis : Theory and Applications, edited by Leif O. Arkeryd, Nigel J. Cutland, C. Ward Henson, (electronic resource)
Link
http://dx.doi.org/10.1007/978-94-011-5544-1
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Foundations of Nonstandard Analysis A Gentle Introduction to Nonstandard Extensions -- 1 Introduction -- 2 Nonstandard Extensions -- 3 Logical Formulas -- 4 Nonstandard Extensions of Multisets -- 5 Nonstandard Extensions of the Multiset (X, P(X)) -- 6 Superstructures -- 7 Saturation -- Nonstandard Real Analysis -- 1 Introduction -- 2 Basic Properties of *? -- 3 Sequences and Series -- 4 Continuity -- 5 Differentiation -- 6 Riemann Integration -- 7 Topology on ? -- 8 Using Internal Subsets of *? -- 9 An Application: Differential Equations -- Nonstandard Analysis and Topology -- 1 Metric and Topological Spaces -- 2 Continuous Mappings -- 3 Convergence -- 4 More on Topologies -- 5 Compact Spaces -- 6 Product Spaces -- 7 Restricted or Relative Topologies -- 8 Uniform Continuity on Metric Spaces -- 9 Nonstandard Hulls -- 10 Compactifications -- 11 More Exercises -- Loeb Measure and Probability -- 1 Introduction -- 2 Finite Loeb Measure -- 3 Constructing Standard Measures -- 4 Representing Standard Measures -- 5 Measurable Functions -- 6 Integration Theory -- 7 Probability Theory -- 8 Advertisement -- 9 Exercises -- An Introduction to Nonstandard Functional Analysis -- 1 Elementary Nonstandard Analysis of Normed Linear Spaces -- 2 Advanced Theory of Banach Spaces -- 3 Elementary Theory of Linear Operators -- 4 Spectral Theory of Bounded Operators -- 5 Applications of Nonstandard Spectral Theory -- 6 Closed Operators -- Applications of Nonstandard Analysis in Ordinary Differential Equations -- 1 Introduction -- 2 Tools in NSA -- 3 Differential Equations and Recursive Sequences -- 4 Regular Perturbations -- 5 Example -- 6 Dynamical Systems: Notions of Stability -- 7 Singular Perturbations -- Better Nonstandard Universes with Applications -- 1 Introduction -- 2 The Isomorphism Property -- 3 The Special Model Axiom and Full Saturation -- 4 The ?-Bolzano-Weierstrass Property -- Internal Martingales and Stochastic Integration -- 1 Hyperfinite Probability Spaces -- 2 Poisson Processes -- 3 Brownian Motion -- 4 Internal Martingales -- 5 Doob's Inequality -- 6 Quadratic Variation -- 7 Standard Parts -- 8 S-continuity -- 9 Stochastic Integration -- 10 Itô's Formula -- 11 Lévy's Characterization of Brownian Motion -- 12 Connections to Standard Theory -- 13 Stochastic Integrals in Higher Dimensions -- 14 Stochastic Differential Equations -- 15 Brownian Local Time -- 16 The Infinite Dimensional Ornstein-Uhlenbeck Process -- Stochastic Differential Equations with Extra Properties -- 1 Introduction -- 2 Spaces of Stochastic Processes -- 3 Solutions of Stochastic Differential Equations -- 4 Solutions which are Markov Processes -- 5 A Fixed Point Theorem -- 6 Stochastic Differential Equations with Nondegenerate Coefficients -- Hyperfinite Mathematical Finance -- 1 Introduction -- 2 Finite Market Models -- 3 Pricing Options in a Hyperfinite CRR Model -- 4 Hyperfinite Trading Strategies -- 5 Convergence of Prices and Strategies -- 6 Further Developments -- Applications of Nsa to Mathematical Physics -- 1 A Kinetic Inequality -- 2 The Time Asymptotic Behaviour for Certain Rarefied Gases when the Incoming Fluxes at the Boundary are Given -- 3 On Semiclassical Limits for the Schrödinger Equation -- A Nonstandard Approach to Hydromechanics Navier-Stokes Equations -- 1 Introduction -- 2 Deterministic Navier-Stokes Equations -- 3 Statistical Solutions -- 4 Stochastic Equations -- 5 Some Open Problems
Dimensions
unknown
Extent
1 online resource (384 pages).
Form of item
online
Isbn
9789401155441
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-94-011-5544-1
Specific material designation
remote
System control number
  • (OCoLC)840311313
  • (OCoLC)ocn840311313

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