Asymptotic properties of realized power variations and related functionals of semimartingales

Details Asymptotic properties of realized power variations and related functionals of semimartingales Asymptotic properties of realized power variations and related functionals of semimartingales

2006-04-20

arxiv.org/abs/math/0604450v1

Mathematics

Probability

Scientific paper

This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is 2 we get the realized quadratic variation) . We prove a variety of ``laws of large numbers'', that is convergence in probability of these sums, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.

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