Rate optimality of wavelet series approximations of fractional Brownian motion

Consider the fractional Brownian motion process B-H (t), t is an element of [0, T], with parameter H is an element of (0, 1). Meyer, Sellan and Taqqu [11] have developed several random wavelet representations for B-H (t), of the form Sigma(k=0)(infinity) U-k (t)is an element of(k) where is an element of(k) are Gaussian random variables and where the functions U-k are not random. Based on the results of Kuhn and Linde [5], we say that the approximation Sigma(k=0)(n) U-k (t)is an element of(k) of B-H (t) is optimal if [EQUATION] as n --> infinity. We show that the random wavelet representations given in Meyer, Sellan and Taqqu [11] are optimal.