A Central Limit Theorem for the Generalized Quadratic Variation of the Step Fractional Brownian Motion

Antoine Ayache (1) , Pierre Bertrand (2) , Jacques Lévy Véhel (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 IJL - Institut Jean Lamour
3 COMPLEX - Artificial Evolution and Fractals

This paper gives a central limit theorem for the generalized quadratic variation of the step fractional Brownian motion. We first recall the denition of this process and the statistical results on the estimation of its parameters.

Mots clés: Generalized quadratic variation.; Generalized quadratic variation; Step fractional Brownian motion; Hurst index; Detection of abrupt changes; Random wavelet series

Domaines: Probabilités [math.PR]

Antoine Ayache, Pierre Bertrand, Jacques Lévy Véhel. A Central Limit Theorem for the Generalized Quadratic Variation of the Step Fractional Brownian Motion. Statistical Inference for Stochastic Processes, 2007, 10 (1), pp.1-27. ⟨10.1007/s11203-005-0532-2⟩. ⟨hal-00539211⟩