We provide an integral representation for smooth functionals of continuous semimartingales. The representation is related to an infinite-dimensional nonautonomous parabolic equation. Semimartingale integral representations, including a martingale representation, are given in terms of a solution to this equation.
Hyungsok Ahn. "Semimartingale integral representation." Ann. Probab. 25 (2) 997 - 1010, April 1997. https://doi.org/10.1214/aop/1024404427