A unified approach to infinite-dimensional integration

DOI10.1142/S0129055X16500057zbMath1339.28018OpenAlexW2963261912MaRDI QIDQ2806158

Sonia Mazzucchi, Sergio A. Albeverio

Publication date: 13 May 2016

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129055x16500057

zbMATH Keywords

stochastic processesFeynman path integralsprobabilistic representation of solutions of PDEsintegration theory via linear functionalsmeasure theory on infinite-dimensional spaces

Mathematics Subject Classification ID

Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05)

Related Items

White noise space analysis and multiplicative change of measures ⋮ An Itô calculus for a class of limit processes arising from random walks on the complex plane ⋮ On the pointwise convergence of the integral kernels in the Feynman-Trotter formula ⋮ A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field ⋮ The average values of a kind of functionals in LP and concentration without measure ⋮ Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections ⋮ An operational construction of the sum of two non-commuting observables in quantum theory and related constructions ⋮ Mathematical theory of Feynman path integrals ⋮ Generalized Feynman path integrals and applications to higher-order heat-type equations ⋮ Probabilistic representation formula for the solution of fractional high-order heat-type equations ⋮ Asymptotics of Gaussian integrals in infinite dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic approximations for probability integrals
• Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
• Stochastic calculus with infinitesimals
• Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations
• The time-dependent quartic oscillator --- a Feynman path integral approach
• An introduction to homological algebra
• Asymptotic expansion of perturbative Chern-Simons theory via Wiener space
• Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
• Open quantum systems and Feynman integrals
• Probabilistic construction of the solution of some higher order parabolic differential equation
• Gaussian measures in Banach spaces
• On the Schrödinger equation with potentials which are Laplace transforms of measures
• Feynman path integrals for polynomially growing potentials
• The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time
• Mesures cylindriques, espaces de Wiener et fonctions aléatoires gaussiennes
• Non-Gaussian analysis and hypergroups
• Semiclassical analysis for diffusions and stochastic processes
• Phase space Feynman path integrals of higher order parabolic type with general functional as integrand
• Markov processes, semigroups and generators.
• An introduction to infinite-dimensional analysis
• Compact systems of sets
• On seminorms and probabilities, and abstract Wiener spaces
• The Trace Formula for the Heat Semigroup with Polynomial Potential
• FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRÖDINGER EQUATION WITH POLYNOMIAL POTENTIAL: A WHITE NOISE APPROACH
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• A unified approach to infinite dimensional integration
• Feynman integrals as Hida distributions: the case of non-perturbative potentials
• On quantum theory in terms of white noise
• Feynman's Path Integrals and Henstock's Non-Absolute Integration
• A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS
• Phase space Feynman path integrals
• A RIGOROUS CONSTRUCTION OF ABELIAN CHERN-SIMONS PATH INTEGRALS USING WHITE NOISE ANALYSIS
• Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces
• Stochastic Partial Differential Equations with Levy Noise
• Measurable Functions on Hilbert Space
• Abstract Wiener processes and their reproducing Kernel Hilbert spaces
• An Introduction to Infinite-dimensional Oscillatory and Probabilistic Integrals
• Mathematical aspects of the quantum theory of fields. Part V. Fields modified by linear homogeneous forces
• Abstract Probability Spaces and a Theorem of Kolmogoroff
• Functional Integration
• Measure and integration theory. Transl. from the German by Robert B. Burckel
• Stochastic Equations in Infinite Dimensions