Asymptotic properties of realized power variations and related functionals of semimartingales

This paper is concerned with the asymptotic behavior of sums of the form , where X is a 1-dimensional semimartingale and f a suitable test function, typically f(x)=xr, as [Delta]n-->0. We prove a variety of "laws of large numbers", that is convergence in probability of Un(f)t, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.

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Year of publication:	2008
Authors:	Jacod, Jean
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 118.2008, 4, p. 517-559
Publisher:	Elsevier
Keywords:	Central limit theorem Quadratic variation Power variation Semimartingale

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008873882