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arXiv · 2606.27839

Factorization of Time-Ordered Exponentials for Wiener Space Transformations

Jirô Akahori·Takafumi Amaba·Tasuku Kubo
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Abstract

We develop an operator-algebraic framework for change-of-variables formulas on Wiener space, interpreting them as arising from hidden symmetries acting on observables. We show that general transformations can be represented by time-ordered exponentials generated by annihilation and creation operators, and that these admit an explicit factorization into a determinant, a multiplication operator, and a translation operator. Taking expectations recovers the classical formulas, including the Ramer--Kusuoka formula.

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BibTeXRIS

Jirô Akahori, Takafumi Amaba, Tasuku Kubo. 2026-06-26. Factorization of Time-Ordered Exponentials for Wiener Space Transformations. https://arxiv.org/abs/2606.27839

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