A study on the discretization of fractional Brownian motion

Date

2020-12-01

Author

Coşkun, Buket
Vardar Acar, Ceren
Demirtaş, Hakan

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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.

URI

https://hdl.handle.net/11511/69630

Journal

INSTITUTE OF PHYSICS CONFERENCE SERIES

DOI

https://doi.org/10.1063/5.0026598

Collections

Department of Statistics, Article

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Citation Formats

B. Coşkun, C. Vardar Acar, and H. Demirtaş, “A study on the discretization of fractional Brownian motion,” INSTITUTE OF PHYSICS CONFERENCE SERIES, pp. 1–6, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69630.