This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for Studentized statistics of power variations.
"Edgeworth expansion for functionals of continuous diffusion processes." Ann. Appl. Probab. 26 (6) 3415 - 3455, December 2016. https://doi.org/10.1214/16-AAP1179