Convergence properties of wavelet series expansions of fractional Brownian motion

We 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. (C) 1996 Academic Press, Inc.