Bulletin of the
Korean Mathematical Society BKMS

In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form $$ F(x)=\hat\nu(( g_1, x)^{\sim}, \ldots, (g_n, x)^{\sim}) $$ defined on a very general function space $C_{a,b}[0,T]$. We also present a change of scale formula for function space integrals of such cylinder functionals.

Keywords: generalized Brownian motion, generalized analytic Feynman integral, function space integral, cylinder functional, change of scale formula

MSC numbers: 60J65, 28C20