EDGEWORTH EXPANSION FOR FUNCTIONALS OF CONTINUOUS DIFFUSION PROCESSES

• 成果类型: Article
• 署名作者: Podolskij, Mark; Yoshida, Nakahiro
• 署名单位: Aarhus University; Japan Science & Technology Agency (JST); Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1179
• 发表日期: 2016
• 页码: 3415-3455
• 关键词: asymptotic expansions; malliavin calculus; distributions

摘要

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.