A study on the discretization of fractional Brownian motion

Coşkun, Buket
Vardar Acar, Ceren
Demirtaş, Hakan
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.

Citation Formats
B. Coşkun, C. Vardar Acar, and H. Demirtaş, “A study on the discretization of fractional Brownian motion,” INSTITUTE OF PHYSICS CONFERENCE SERIES, vol. 2293, no. 180013, pp. 1–6, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69630.