Summary
For a fractional Brownian motion B H on [0,1], we consider approximations of B H by piecewise polynomial splines. Asymptotics of minimal average error rates are established and found to be of order k -H, where k is the number of free knots used in the spline approximation.
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Creutzig, J., Lifshits, M. (2008). Free-Knot Spline Approximation of Fractional Brownian Motion. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_10
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DOI: https://doi.org/10.1007/978-3-540-74496-2_10
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