Journal of the
Korean Mathematical Society JKMS

In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.

Keywords: Generalized Brownian process, modified generalized integral transform, modified convolution product, first variation, translation theorem, Cameron-Strovick type theorem

MSC numbers: Primary 60J65, 28C20, 44A15, 46C07

Supported by: The work was supported by the research fund of Dankook University in 2020.