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Edgeworth expansion for functionals of continuous diffusion processes

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  • Mark Podolskij
  • Nakahiro Yoshida, CREST Japan Science and Technology Agency, The Institute of Statistical Mathematics, Graduate School of Mathematical Science, Japan
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.
Original languageEnglish
JournalAnnals of Applied Probability
Pages (from-to)3415-3455
Publication statusPublished - 21 Jan 2016

    Research areas

  • math.PR, stat.ME, 62M09, 60F05, 62H12

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