Forschungsseminar der Wahrscheinlichkeitstheorie: "LAN property of statistical models with Lévy driven processes observed at high frequency: Malliavin calculus approach."

15.05.2015, 14:15-15:45  –  Am Neuen Palais, Haus 22 Raum 1.27
Forschungsseminar Wahrscheinlichkeitstheorie

Alexei Kulik (Kyiv)

Suppose we have a high-frequency sample for the solution to a SDE dX_t^?=a(?_1,X^?_t) dt+ ?_2 d Z_t+dU_t, where Z is a locally ?-stable symmetric process, and U is a Lévy process, which has the meaning of a ``nuisance noise''. We will derive the local asymptotic normality (LAN) property of the model, using a Malliavin calculus-based integral representation for the derivative of the log-likelihood function of the model.