A space of generalized Brownian motion path-valued continuous functions with application

In this paper, we introduce the paths space ${\mathcal{C}}_0^{\mathrm{g}\mathrm{B}\mathrm{m}}$ which is consists of generalized Brownian motion path-valued continuous functions on $[0,T]$. We next present several relevant examples of the paths space integral. We then discuss the concept of the analytic Feynman integration theory for functionals $F$ on the paths space ${\mathcal{C}}_0^{\mathrm{g}\mathrm{B}\mathrm{m}}$.