Translation Theorem for Function Space Integral Associated with Gaussian Paths and Applications

Cameron–Storvick theorem associated with Gaussian paths on function space

“…In order to present our Cameron-Storvick theorem on the function space C a,b [0, T ], we follow the exposition of [4,5,7].…”

“…In order to establish an integration by parts formula for the function space integral associated with Gaussian paths on C a,b [0, T ] , we need a translation theorem for the function space integral. The following translation theorem is due to Chang and Choi [4].…”

“…The framework and methods we used to obtain the results in [4][5][6][7][8][9]14] and this article are very dependent upon results in the book [22] by Yeh concerning noncentered Gaussian processes, that is, GBMP.…”

“…T ] may also be found in [4,5]. In particular, we refer to the reference [7] for the definition and the properties of the Gaussian processes Z k used in this paper.…”

Cameron-Storvick theorem associated with Gaussian paths on function space

“…We also assume familiarity with [6,8] and adopt the notation and terminologies of those papers. The basic concepts and definitions of the function space (C a,b [0, T ], W(C a,b [0, T ]), µ), which forms a complete probability space, the concept of the scale-invariant measurability on C a,b [0, T ], the Cameron-Martin space C ′ a,b [0, T ] and the PWZ stochastic integral on C a,b [0, T ] may also be found in [4,5]. In particular, we refer to the reference [7] for the definition and the properties of the Gaussian processes Z k used in this paper.…”