Weighted power variations of fractional Brownian motion and application to approximating schemes
نویسندگان
چکیده
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 ∈ (0, 1). The behaviour is different when H < 1/2 and powers are odd, compared with the case when H = 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.
منابع مشابه
Convergence of weighted power variations of fractional Brownian motion
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 ∈ (0, 1). The behaviour is different when H < 1/2 and powers are odd, compared with the case when H = 1/2 or when H > 1/2 and powers are even. In the second part, one applies the results of the first part to compute the exact rate of convergen...
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