The allure of infinitesimals: Sergio Albeverio and nonstandard analysis

DOI10.1007/978-3-031-14031-0_9OpenAlexW4362503511MaRDI QIDQ6196935

Tom Lindstrøm

Publication date: 15 March 2024

Published in: Quantum and Stochastic Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-14031-0_9

zbMATH Keywords

nonstandard analysismathematical physicsstochastic analysis

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Quantum field theory; related classical field theories (81Txx) Other applications of nonstandard models (economics, physics, etc.) (03H10)

Cites Work

• Stochastic calculus with infinitesimals
• First steps towards an equilibrium theory for Lévy financial markets
• Foundations of infinitesimal stochastic analysis
• Existence of time evolutions of non-equilibrium states in statistical mechanics
• Chasse au canard
• Gaussian and non-Gaussian random fields associated with Markov processes
• Polynomials of the occupation field and related random fields
• A hyperfinite flat integral for generalized random fields
• An action functional for Lévy Brownian motion
• A nonstandard Lévy-Khintchine formula and Lévy processes
• Hyperfinite stochastic integration for Lévy processes with finite-variation jump part
• Nonlinear stochastic integrals for hyperfinite Lévy processes
• A nonstandard construction of Lévy Brownian motion
• Infinitesimal methods in control theory: deterministic and stochastic
• Examples of extremal lattice fields without the global Markov property
• Nonstandard conditions for the global Markov property for lattice fields
• Markov type properties for mixtures of probability measures
• Attractiveness of interactions for binary lattice systems and the global Markov property
• Applications of nonstandard analysis to spin models
• On Edwards' model for long polymer chains
• On Edwards' model for polymer chains. II: The self-consistent potential
• Bounds on the oscillation of spin systems
• On Edwards' model for polymer chains. III. Borel summability
• A non-standard representation for Brownian motion and Ito integration
• The discrete Einstein relation
• Loeb measures in practice: Recent advances. EMS lectures 1997
• Brownian motion on the Wiener sphere and the infinite-dimensional Ornstein-Uhlenbeck process
• Singular traces and compact operators
• The Wiener sphere and Wiener measure
• Lifting Lévy processes to hyperfinite random walks
• Hyperfinite Dirichlet forms and stochastic processes
• Optimisation of measures on a hyperfinite adapted probability space
• The moment problem on the Wiener space
• Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos
• A mathematical flat integral realization and a large deviation result for the free Euclidean field
• An infinitesimal approach to stochastic analysis
• Nonstandard Construction of the Stochastic Integral and Applications to Stochastic Differential Equations.I
• Fractional Brownian Fields as Integrals of White Noise
• Martingale property of empirical processes
• A combinatorial infinitesimal representation of Lévy processes and an application to incomplete markets
• Infinitesimals in Action
• On Hyperfinite Representations of Distributions
• Radically Elementary Probability Theory. (AM-117)
• Singular Perturbations and Nonstandard Analysis
• Hyperdefinite stochastic integration I: The nonstandard theory.
• A singular Sturm-Liouville problem treated by non-standard analysis.
• Nonstandard Analysis and Lattice Statistical Mechanics: A Variational Principle
• A Loeb-Measure Approach to Theorems by Prohorov, Sazonov and Gross
• On homogeneous chaos
• The Brownian bridge as a flat integral
• On large deviations in Hilbert space
• Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory
• Internal set theory: A new approach to nonstandard analysis
• Brownian motion on nested fractals
• Brownian motion on simple fractal spaces
• STOCHASTIC NAVIER–STOKES EQUATIONS: LOEB SPACE TECHNIQUES & ATTRACTORS
• Hyperfinite Lévy Processes
• Corrigendum and addendum to ‘hyperfinite Lévy processes’ by Tom Lindstrøm (Stochastics 76(6):517–548, 2004)
• Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion
• Invariance principles for Brownian intersection local time and polymer measures.
• An extension of the ventcel- freidlin large deviation principle
• Non-standard analysis
• Perturbations of the Schrödinger equation by potentials with small support
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