Before revision:  By computing the asymptotic behavior of the autocovariance and of the spectral density , we find that the quantized process has the same Hurst exponent of the original process.
After revision:  By computing the asymptotic behavior of the autocovariance and of the spectral density of the discretized process (i.e. the process with round-off error) are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the quantized process has the same Hurst exponent of the original process.