| Weighted power variations of fractional Brownian motion and application to approximating schemes (2007) | |||||||||||||
Abstract | |||||||||||||
| The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion $B$ with Hurst index $H\in(0,1)$. The behaviour is different when $ H < \nicefrac{1}{2}$ and powers are odd, compared with the case when $H=\nicefrac{1}{2}$. In the second part, one applies the results of the first part to compute the exact rate of convergence of some approximating schemes associated to scalar stochastic differential equations driven by $B$. The limit of the error between the exact solution and the considered scheme (whose size depends on the Hurst index $H$) is computed explicitly. | |||||||||||||
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