Conditional function space integrals with applications

DOI10.1216/rmjm/1181072102zbMath0864.28006OpenAlexW1985275686MaRDI QIDQ1915742

Dong Myung Chung, Seung Jun Chang

Publication date: 17 June 1997

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL26-1/contents/contents.htm

zbMATH Keywords

conditional Wiener integralCameron-Martin type translation theoremKac-Feynman integral equationconditional function space integral

Mathematics Subject Classification ID

Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11)

Related Items (28)

Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral ⋮ Generalized conditional transform with respect to the Gaussian process on function space ⋮ Generalized integral transforms with the translation operator on function space ⋮ A new approach method to obtain theL₁generalized analytic Fourier–Feynman transform ⋮ \(L_2\)-sequential transforms on function space ⋮ A modified analytic function space Feynman integral and its applications ⋮ An analytic operator-valued generalized Feynman integral on function space ⋮ Some basic relationships among transforms, convolution products, first variations and inverse transforms ⋮ New expressions of the modified generalized integral transform via the translation theorem with applications ⋮ Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications ⋮ Evaluation formulas for generalized conditional Wiener integrals with drift on a function space ⋮ Generalized analytic Fourier-Feynman transform of functionals in a Banach algebra \(\mathcal F^{a,b}_{A_{1},A_{2}}\) ⋮ Analogues of conditional Wiener integrals with drift and initial distribution on a function space ⋮ Change of path formula on the function space with applications ⋮ Relationships Involving Transforms and Convolutions Via the Translation Theorem ⋮ Translation theorems for the Fourier-Feynman transform on the product function space \(C_{a,b}^2[0,T\)] ⋮ Parts formulas involving conditional generalized Feynman integrals and conditional generalized Fourier–Feynman transforms on function space ⋮ The linear space of generalized Brownian motions with applications ⋮ Sequential generalized transforms on function space ⋮ A TRANSLATION THEOREM FOR THE GENERALISED ANALYTIC FEYNMAN INTEGRAL ASSOCIATED WITH GAUSSIAN PATHS ⋮ A modified analytic function space Feynman integral of functionals on function space ⋮ Unnamed Item ⋮ Integral transforms of functionals in \(L^{2}(C_{a,b}[0,T)\)] ⋮ Fundamental formulas for modified generalized integral transforms ⋮ A new aspect of the analytic Fourier-Feynman transform and its applications ⋮ Translation theorem for function space integral associated with Gaussian paths and applications ⋮ Evaluation Formulas for Conditional Function Space Integrals I ⋮ Relationships between the *_w-product and the generalized integral transforms

Cites Work

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• A simple formula for conditional Wiener integrals with applications
• Frechet-Volterra variational equations, boundary value problems, and function space integrals
• Transformations of Wiener integrals under translations
• Evaluation formulas for conditional abstract wiener integrals
• On Distributions of Certain Wiener Functionals
• Additive Functionals on a Space of Continuous Functions. I

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