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

Abstract

In this paper we establish a more general translation theorem for function space integral associated with Gaussian paths on the function space $$C_{a,b}[0,T]$$ . The function space $$C_{a,b}[0,T]$$ is induced by a generalized Brownian motion process. Thus, the Gaussian processes used in this paper are non-centered processes. We next apply our fundamental translation theorem to the generalized Fourier–Feynman transforms. We then proceed to show that these general translation theorems for the generalized Fourier–Feynman transforms can be applied to two well-known classes of functionals on the function space $$C_{a,b}[0,T]$$ .