Wiener integrals with respect to the Hermite process and a Non-Central Limit Theorem

Makoto Maejima (1) , Ciprian A. Tudor (2, 3)

1 Department of Mathematics
2 CES - Centre d'économie de la Sorbonne
3 SAMOS - Statistique Appliquée et MOdélisation Stochastique

We introduce Wiener integrals with respect to the Hermite process and we prove a Non-Central Limit Theorem in which this integral appears as limit. As an example, we study a generalization of the fractional Ornstein-Uhlenbeck process.

Domaines: Probabilités [math.PR]

Makoto Maejima, Ciprian A. Tudor. Wiener integrals with respect to the Hermite process and a Non-Central Limit Theorem. Stochastic Analysis and Applications, 2007, 25 (5), pp.1043 - 1056. ⟨10.1080/07362990701540519⟩. ⟨hal-00176227⟩