A study on the discretization of fractional Brownian motion

In this study, we first discretize the fractional Brownian motion in time and observe multivariate Gaussian random variables (mGrv) to have a fractional Gaussian noise (fGn). Afterwards, we have discretized this discrete time process in space using a discretization proportion p and observe a random walk. We carry out this simulation study to foresee whether the correlated random walk using certain discretization parameters p behave similar to fBm. Based on this simulation study, we conclude on two important conjectures. First, there should exist a correlated random walk with parameter p converging to fBm since there exist correlated random walks behaving very similar to its originating fBm. Second, the convergence is satisfied for only certain values of p