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Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

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Abstract

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space (H, B, v). An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B. Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class ℱ(B) and we finally investigate some Fubini theorems involving CFFT.

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Acknowledgement

The authors would like to express their gratitude to the editor and the referees for their valuable comments and suggestions which have improved the original paper. Sang Kil Shim worked as the leading author.

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Authors and Affiliations

  1. School of General Education, Dankook University, Cheonan, Republic of Korea

    Jae Gil Choi

  2. Department of Mathematics, Dankook University, Cheonan, Republic of Korea

    Sang Kil Shim

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  1. Jae Gil Choi
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  2. Sang Kil Shim
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Correspondence to Jae Gil Choi.

Additional information

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1062770).

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Choi, J.G., Shim, S.K. Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space. Czech Math J 73, 849–868 (2023). https://doi.org/10.21136/CMJ.2023.0310-22

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