Asymptotic properties of power variations of L\'evy processes
Abstract
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'evy process. One can completely elucidate the first order behavior (convergence in probability, possibly after normalization). As for the associated CLT, one can show some versions of it, but only in a limited number of cases. In some other cases, a CLT just does not exist.
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