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Milstein’s type schemes for fractional SDEs. (English) Zbl 1197.60070
Summary: Weighted power variations of fractional Brownian motion \(B\) are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations driven by \(B\). The limit of the error between the exact solution and the considered scheme is computed explicitly.

MSC:
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60F15 Strong limit theorems
60G22 Fractional processes, including fractional Brownian motion
60H05 Stochastic integrals
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