Convergence Properties of Wavelet Series Expansions of Fractional Brownian Motion

AbstractWe consider the approximation of a fractional Brownian motion by a wavelet series expansion at resolution 2−l. The approximation error is measured in the integrated mean squared sense over finite intervals and we obtain its expansion as a sum of terms with increasing rates of convergence. The dependence of the coefficients in the expansion of the error on the scale function is explicitly determined