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 Conditional transform with respect to the Gaussian process involving the conditional convolution product and the first variation Bull. Korean Math. Soc. 2014 Vol. 51, No. 6, 1561-1577 https://doi.org/10.4134/BKMS.2014.51.6.1561Published online November 30, 2014 Hyun Soo Chung, Il Yong Lee, and Seung Jun Chang Dankook University, Dankook University, Dankook University Abstract : In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals $F$ in $S_{\alpha}$ \cite{HJS12, HV11}. Keywords : Brownian motion process, Wiener integral, Gaussian process, conditional convolution product, simple formula, conditional transform with respect to Gaussian process MSC numbers : Primary 60J25, 28C20 Downloads: Full-text PDF