Bulletin of the
Korean Mathematical Society BKMS

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