Displaying similar documents to “Convergence of Submartingales to an Increasing Process under Discretization of Filtrations”

Asymptotic properties of power variations of Lévy processes

Jean Jacod (2007)

ESAIM: Probability and Statistics

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We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function  evaluated at the increments of a Lévy process between the successive times Δ for = 0,1,...,. One can elucidate completely the first order behavior, that is the convergence in probability of such sums, possibly after normalization and/or centering: it turns out that there is a rather wide variety of possible behaviors, depending on the structure of jumps and on the...