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2004•Rocky Mountain Journal of MathematicsOpen access

A Change of Scale Formula for Wiener Integrals of Unbounded Functions

Inkyu Yoo, Teuk-Seob Song, B.S. Kim, Kun-Soo Chang

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Abstract

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S on classical Wiener space.Yoo and Skoug extended these results to abstract Wiener space for a more generalized Fresnel class F A 1 ,A 2 than the Fresnel class F (B) which corresponds to the Banach algebra S on classical Wiener space.In this paper we present a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous.

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Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S on classical Wiener space.Yoo and Skoug extended these results to abstract Wiener space for a more generalized Fresnel class F A 1 ,A 2 than the Fresnel class F (B) which corresponds to the Banach algebra S on classical Wiener space.In this paper we present a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous.

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Available abstract

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S on classical Wiener space.Yoo and Skoug extended these results to abstract Wiener space for a more generalized Fresnel class F A 1 ,A 2 than the Fresnel class F (B) which corresponds to the Banach algebra S on classical Wiener space.In this paper we present a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous.

Key concepts: Classical Wiener space, Integral representation theorem for classical Wiener space, Mathematics, Feynman integral, Bounded function, Banach space, Banach algebra, Class (philosophy)

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