# Convergence of some random functionals of discretized semimartingales

Abstract : In this paper, we study the asymptotic behavior of sums of functions of the increments of a given semimartingale, taken along a regular grid whose mesh goes to $0$. The function of the $i$th increment may depend on the current time, and also on the past of the semimartingale before this time. We study the convergence in probability of two types of such sums, and we also give associated central limit theorems. This extends known results when the summands are a function depending only on the increments, and this is motivated mainly by statistical applications.
Keywords :
Type de document :
Pré-publication, Document de travail
31 pages. 2010
Domaine :

https://hal.archives-ouvertes.fr/hal-00446609
Contributeur : Assane Diop <>
Soumis le : mercredi 13 janvier 2010 - 11:56:59
Dernière modification le : mercredi 21 mars 2018 - 18:56:48
Document(s) archivé(s) le : vendredi 18 juin 2010 - 00:47:36

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• HAL Id : hal-00446609, version 1
• ARXIV : 1001.2182

### Citation

Assane Diop. Convergence of some random functionals of discretized semimartingales. 31 pages. 2010. 〈hal-00446609〉

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