# Asymptotic properties of power variations of Lévy processes

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 173-196
- ISSN: 1292-8100

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topJacod, Jean. "Asymptotic properties of power variations of Lévy processes." ESAIM: Probability and Statistics 11 (2007): 173-196. <http://eudml.org/doc/250133>.

@article{Jacod2007,

abstract = {
We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function f evaluated at the increments of a Lévy process between
the successive times iΔn for i = 0,1,...,n. 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 chosen test function f. As for the associated central limit theorem,
one can show some versions of it, but unfortunately in a limited number of cases only: in some other cases a CLT just does not exist.
},

author = {Jacod, Jean},

journal = {ESAIM: Probability and Statistics},

keywords = {Central limit theorem; quadratic variation; power variation; Lévy processes.; central limit theorem; Lévy processes},

language = {eng},

month = {6},

pages = {173-196},

publisher = {EDP Sciences},

title = {Asymptotic properties of power variations of Lévy processes},

url = {http://eudml.org/doc/250133},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Jacod, Jean

TI - Asymptotic properties of power variations of Lévy processes

JO - ESAIM: Probability and Statistics

DA - 2007/6//

PB - EDP Sciences

VL - 11

SP - 173

EP - 196

AB -
We determine the asymptotic behavior of the realized power variations, and more generally of sums of a given function f evaluated at the increments of a Lévy process between
the successive times iΔn for i = 0,1,...,n. 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 chosen test function f. As for the associated central limit theorem,
one can show some versions of it, but unfortunately in a limited number of cases only: in some other cases a CLT just does not exist.

LA - eng

KW - Central limit theorem; quadratic variation; power variation; Lévy processes.; central limit theorem; Lévy processes

UR - http://eudml.org/doc/250133

ER -

## References

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