Sang Kil Shim, Ae Young Ko, Jae Gil Choi: Fubini theorem for conditional Fourier-Feynman transforms associated with random vectors, 113-126

Abstract:

In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) on the Wiener space. We establish the existence of the CFFT for bounded functionals which form a Banach algebra. We then investigate Fubini theorems for the CFFT. The Fubini theorems for the transforms investigated in this paper are to express the iterated CFFT as a single CFFT. The conditioning functions in the Fubini theorems are uncorrelated finite-dimensional random vectors on the Wiener space.

Key Words: Wiener space, conditional Fourier-Feynman transform, uncorrelated random vector, Fubini theorem.

2020 Mathematics Subject Classification: Primary 46B09, 46G12; Secondary 28C20.

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