A GENERALIZED CORRELATED RANDOM WALK APPROXIMATION TO FRACTIONAL BROWNIAN MOTION

In this study, we mainly propose an algorithm to generate correlated random walk converging to fractional Brownian motion, with Hurst parameter, H∈ [1/2,1]. The increments of this random walk are simulated from Bernoulli distribution with proportion p, whose density is constructed using the link between correlation of multivariate Gaussian random variables and correlation of their dichotomized binary variables. We prove that the normalized sum of trajectories of this proposed random walk yields a Gaussian process whose scaling limit is the fractional Brownian motion