A Cameron-Storvick theorem for the analytic Feynman integral associated with Gaussian paths on a Wiener space and applications

DOI10.3934/cpaa.2018106zbMath1396.28027OpenAlexW2807368615WikidataQ129685714 ScholiaQ129685714MaRDI QIDQ1660050

Jae Gil Choi, Seung Jun Chang

Publication date: 23 August 2018

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2018106

zbMATH Keywords

Gaussian processPaley-Wiener-Zygmund stochastic integralCameron-Storvick theoremgeneralized analytic Feynman integraltranslation theorem

Mathematics Subject Classification ID

Gaussian processes (60G15) Brownian motion (60J65) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (3)

Parts formulas involving the Fourier-Feynman transform associated with Gaussian paths on Wiener space ⋮ Analytic Fourier-Feynman transforms associated with bounded linear operators on abstract Wiener spaces ⋮ Change of path formula for generalized Wiener integral with applications

Cites Work

• Notes on the Feynman integral. II
• A Kac-Feynman integral equation for conditional Wiener integrals
• Integration by parts for abstract Wiener measures
• Fourier-Feynman transforms and the first variation
• Generalized Feynman integrals via conditional Feynman integrals
• Abstract Wiener spaces and applications to analysis
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Transformations of Wiener integrals under translations
• A MULTIPLE GENERALIZED FOURIER–FEYNMAN TRANSFORM VIA A ROTATION ON WIENER SPACE
• A Note on Paley-Wiener-Zygmund Stochastic Integrals
• Gaussian Hilbert Spaces
• Relationships involving generalized fourier–feynman transform, convolution and first variation
• A Translation Theorem for Analytic Feynman Integrals
• Additive Functionals on a Space of Continuous Functions. I
• The First Variation of an Indefinite Wiener Integral
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