Asymptotic properties of power variations of Lévy processes

Details Asymptotic properties of power variations of Lévy processes Asymptotic properties of power variations of Lévy processes

2005-11-02

arxiv.org/abs/math/0511052v1

Mathematics

Probability

Scientific paper

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\'{e}vy 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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