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December 2016 Edgeworth expansion for functionals of continuous diffusion processes
Mark Podolskij, Nakahiro Yoshida
Ann. Appl. Probab. 26(6): 3415-3455 (December 2016). DOI: 10.1214/16-AAP1179

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 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.

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Mark Podolskij. Nakahiro Yoshida. "Edgeworth expansion for functionals of continuous diffusion processes." Ann. Appl. Probab. 26 (6) 3415 - 3455, December 2016. https://doi.org/10.1214/16-AAP1179

Information

Received: 1 November 2013; Revised: 1 May 2015; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 06687414
MathSciNet: MR3582807
Digital Object Identifier: 10.1214/16-AAP1179

Subjects:
Primary: 60F05 , 62H12 , 62M09
Secondary: 60G44 , 62G20

Keywords: Diffusion processes , Edgeworth expansion , high frequency observations , power variation

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 2016
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