  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
second order 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.
