Convergence of some random functionals of discretized semimartingales

Assane Diop (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Semimartingale; Contrast functions; Power variation; Limit theorems; Semimartingale.

Domaines: Probabilités [math.PR]

Assane Diop. Convergence of some random functionals of discretized semimartingales. 2010. ⟨hal-00446609⟩