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2020•SymmetryOpen access

A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space

Young Sik Kim

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Abstract

We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.

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We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.

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Available abstract

We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.

Key concepts: Classical Wiener space, Integral representation theorem for classical Wiener space, Feynman integral, Mathematics, Product (mathematics), Class (philosophy), Scale (ratio), Pure mathematics

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