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2014•Journal of the Chungcheng Mathematical SocietyOpen access

RELATIONSHIP BETWEEN THE WIENER INTEGRAL AND THE ANALYTIC FEYNMAN INTEGRAL OF CYLINDER FUNCTION

Byoung Soo Kim

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Abstract

Cameron and Storvick discovered a change of scale formula for Wiener integral of functionals in a Banach algebra $\mathcal{S}$ on classical Wiener space. We express the analytic Feynman integral of cylinder function as a limit of Wiener integrals. Moreover we obtain the same change of scale formula as Cameron and Storvick's result for Wiener integral of cylinder function. Our result cover a restricted version of the change of scale formula by Kim.

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Cameron and Storvick discovered a change of scale formula for Wiener integral of functionals in a Banach algebra $\mathcal{S}$ on classical Wiener space. We express the analytic Feynman integral of cylinder function as a limit of Wiener integrals. Moreover we obtain the same change of scale formula as Cameron and Storvick's result for Wiener integral of cylinder function. Our result cover a restricted version of the change of scale formula by Kim.

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Available abstract

Cameron and Storvick discovered a change of scale formula for Wiener integral of functionals in a Banach algebra $\mathcal{S}$ on classical Wiener space. We express the analytic Feynman integral of cylinder function as a limit of Wiener integrals. Moreover we obtain the same change of scale formula as Cameron and Storvick's result for Wiener integral of cylinder function. Our result cover a restricted version of the change of scale formula by Kim.

Key concepts: Integral representation theorem for classical Wiener space, Feynman integral, Classical Wiener space, Mathematics, Functional integration, Cylinder, Stochastic integral, Mathematical analysis

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RELATIONSHIP BETWEEN THE WIENER INTEGRAL AND THE ANALYTIC FEYNMAN INTEGRAL OF CYLINDER FUNCTION — Research Paper | ScholarLens