Bull. Korean Math. Soc. 2023; 60(5): 1221-1235
Online first article July 19, 2023 Printed September 30, 2023
https://doi.org/10.4134/BKMS.b220602
Copyright © The Korean Mathematical Society.
Jae Gil Choi, Sang Kil Shim
Dankook University; Dankook University
In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier--Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.
Keywords: Wiener space, conditional Fourier--Feynman transform, conditional convolution product, Paley--Wiener--Zygmund stochastic integral
MSC numbers: Primary 28C20, 46G12; Secondary 60J65
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