Semimartingale functions of a class of diffusion processes

This paper obtains the necessary and sufficient conditions on the function f = (f(t,x), t greater than or equal to 0, x is an element of R) for which the transformed process f = f(t,xit) will be a semimartingale (or the It (o) over cap process) for any diffusion process xi with measurable bounded coefficients and uniformly nondegenerate Holder diffusion.