Generalized Feynman path integrals and applications to higher-order heat-type equations
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Publication:1756146
DOI10.1016/j.exmath.2018.09.001zbMath1409.58003OpenAlexW2889610191MaRDI QIDQ1756146
N. Cangiotti, Sergio A. Albeverio, Sonia Mazzucchi
Publication date: 11 January 2019
Published in: Expositiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.exmath.2018.09.001
One-parameter semigroups and linear evolution equations (47D06) Integral representations of solutions to PDEs (35C15) Applications of manifolds of mappings to the sciences (58D30) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Linear higher-order PDEs (35G05)
Related Items (6)
Phase space Feynman path integrals of parabolic type on the torus as analysis on path space ⋮ A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field ⋮ Phase space path integral on torus for the fundamental solution of higher-order parabolic equations ⋮ Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections ⋮ Higher-order heat equation and the Gelfand-Dickey hierarchy ⋮ Mathematical theory of Feynman path integrals
Cites Work
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- Convergence in \(L^{p}\) for Feynman path integrals
- Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
- Stochastic calculus with infinitesimals
- Stochastic analysis without probability: study of some basic tools
- Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations
- The time-dependent quartic oscillator --- a Feynman path integral approach
- Infinite dimensional oscillatory integrals as projective systems of functionals
- Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations
- Generalized Brownian functionals and the Feynman integral
- Open quantum systems and Feynman integrals
- Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques
- Probabilistic construction of the solution of some higher order parabolic differential equation
- Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
- Quasi-invariance of measures under translation
- A signed measure on path space related to Wiener measure
- Iterated processes and their applications to higher order differential equations
- The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
- Conditional maximal distributions of processes related to higher-order heat-type equations
- Remarks on the operator-norm convergence of the Trotter product formula
- Feynman path integrals for polynomially growing potentials
- Semiclassical analysis for diffusions and stochastic processes
- Phase space Feynman path integrals of higher order parabolic type with general functional as integrand
- Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
- Rigorous time slicing approach to Feynman path integrals
- An Itô calculus for a class of limit processes arising from random walks on the complex plane
- Mathematical theory of Feynman path integrals. An introduction
- Generalized Fresnel integrals
- High order heat-type equations and random walks on the complex plane
- The Doss trick on symmetric spaces
- A signed measure on rough paths associated to a PDE of high order: results and conjectures
- Functional integration
- A unified approach to infinite-dimensional integration
- A white noise approach to phase space Feynman path integrals
- Probability representations of solutions of the Cauchy problem for quantum mechanical equations
- A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
- On the Product of Semi-Groups of Operators
- A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s
- Gibbs measures on Brownian currents
- Functional Integration and Partial Differential Equations. (AM-109)
- A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS
- A unified approach to infinite dimensional integrals of probabilistic and oscillatory type with applications to Feynman path integrals
- Wiener measures for path integrals with affine kinematic variables
- Oscillatory integrals, lagrange immersions and unfolding of singularities
- Phase space Feynman path integrals
- Hamiltonian Feynman path integrals via the Chernoff formula
- Feynman Integrals and the Schrödinger Equation
- Space-Time Approach to Non-Relativistic Quantum Mechanics
- Feynman path integrals for the inverse quartic oscillator
- Generalized Measures in Function Spaces
- An Introduction to Infinite-dimensional Oscillatory and Probabilistic Integrals
- Functional Integration
- Projective limits of complex measures and martingale convergence
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