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2006•Communications of the Korean Mathematical SocietyOpen access

CHANGE OF SCALE FORMULAS FOR WIENER INTEGRAL OVER PATHS IN ABSTRACT WIENER SPACE

Byoungsoo Kim, Tae-Soo KIM

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Abstract

Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over $C_0(B)$ as a limit of Wiener integrals over $C_0(B)$ and establish change of scale formulas for Wiener integrals over $C_0(B)$ for some functionals.

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Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over $C_0(B)$ as a limit of Wiener integrals over $C_0(B)$ and establish change of scale formulas for Wiener integrals over $C_0(B)$ for some functionals.

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Available abstract

Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over $C_0(B)$ as a limit of Wiener integrals over $C_0(B)$ and establish change of scale formulas for Wiener integrals over $C_0(B)$ for some functionals.

Key concepts: Classical Wiener space, Integral representation theorem for classical Wiener space, Mathematics, Feynman integral, Scale (ratio), Wiener process, Transformation (genetics), Functional integration

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