A study on the discretization of fractional Brownian motion

COŞKUN B., VARDAR ACAR C., Demirtas H.

AIP Conference Proceedings, cilt.2293, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2293
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1063/5.0026598
  • Dergi Adı: AIP Conference Proceedings
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Artic & Antarctic Regions, Communication Abstracts, INSPEC, Metadex, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.