Relations of Fractional Brownian Motion and Hurst Exponent

We discussed the theoretical foundation of the R/S analysis,that were related Hurst Exponent to self-correlation and self-similarity of the fractional Brownian motion as well as autocorrelation index,self-similarity,long memory of the fractional Gaussian noise series.These are verified that fractional Brownian motion is not Markov processes in case H≠1/2,as well as Hurst index is same as its self-similarity index.The relationship between the long memory Fractional Gaussian noise and Hurst Exponent is obtained,which can determine whether there is a long memory of the sequence via Hurst index.