Commun. Korean Math. Soc. 2009; 24(3): 397-413
Printed September 1, 2009
https://doi.org/10.4134/CKMS.2009.24.3.397
Copyright © The Korean Mathematical Society.
Seung Jun Chang and Jae Gil Choi
Dankook University
In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.
Keywords: generalized Brownian motion process, generalized Fourier-Feynman transform, convolution product, conditional generalized Fourier-Feynman transform, conditional convolution product
MSC numbers: Primary 60J65, 28C20
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