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Asymptotic properties of realized power variations and related functionals of semimartingales

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  • Jacod, Jean

Abstract

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.

Suggested Citation

  • Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:4:p:517-559
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    References listed on IDEAS

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    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    2. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
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