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Statistical Inference for Stochastic Processes 10, 1 (2007) 1-27
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A Central Limit Theorem for the Generalized Quadratic Variation of the Step Fractional Brownian Motion
Antoine Ayache1, Pierre Bertrand2, Jacques Lévy Véhel3

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.
1 :  LPP - Laboratoire Paul Painlevé
2 :  IJL - Institut Jean Lamour : Matériaux -Métallurgie - Nanosciences - Plasma - Surfaces
3 :  INRIA Rocquencourt - COMPLEX
Step fractional Brownian motion – Hurst index – Detection of abrupt changes – Random wavelet series – Generalized quadratic variation.