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.2014.51.6.1561
Published 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
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