Edgeworth expansion for functionals of continuous diffusion processes
Probability
2013-09-10 v1 Methodology
Abstract
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.
Cite
@article{arxiv.1309.2071,
title = {Edgeworth expansion for functionals of continuous diffusion processes},
author = {Mark Podolskij and Nakahiro Yoshida},
journal= {arXiv preprint arXiv:1309.2071},
year = {2013}
}