Semimartingale Functions of a Class of Diffusion Processes
Michael Mania, R. Tevzadae · Theory of Probability and Its Applications · 2001
This paper obtains the necessary and sufficient conditions on the function $f=(f(t,x),\ t\ge0,\ x\in \bf{R})$ for which the transformed process $f=f(t,\xi_t)$ will be a semimartingale (or the Ito process) for any diffusion process $\xi$ with measurable bounded coefficients and uniformly nondegenerate Hölder diffusion.