Variations and estimators for the selfsimilarity order through Malliavin calculus

Ciprian A. Tudor (1, 2) , Frederi Viens (3)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 Department of Statistics [West Lafayette]

Using multiple stochastic integrals, we analyze the asymptotic behavior of quadratic variations for Gaussian and non-Gaussian selfsimilar processes. We apply our results to the study of statistical estimators for the selfsimilarity index.

Mots clés: multiple stochastic integrals; Malliavin calculus; Hermite process; fractional Brownian motion; non-central limit theorems; quadratic variations

Domaines: Probabilités [math.PR]; Théorie [stat.TH]; Statistiques [math.ST]

Ciprian A. Tudor, Frederi Viens. Variations and estimators for the selfsimilarity order through Malliavin calculus. Annals of Probability, 2009, 37 (6), pp.2093-2134. ⟨hal-00174730v2⟩