Quality of synthesis and analysis methods for fractional Brownian motion

Abstract

The article compares the quality of synthesis and analysis methods for fractional Brownian motion (fBm). Three conditions are necessary and sufficient for a process to be fBm. This allows one to check the correspondence between a given synthesis method and the fBm model. Two synthesis methods among 6 tested give good results. Reference signals obtained by these 2 methods are used to evaluate 8 analysis methods. Three estimators have a low bias and a variance close to the Cramer-Rao lower bound.