Information geometric characterization of the complexity of fractional Brownian motions

Linyu Peng, Huafei Sun, Guoquan Xu

研究成果: Article査読

12 被引用数 (Scopus)

抄録

The complexity of the fractional Brownian motions is investigated from the viewpoint of information geometry. By introducing a Riemannian metric on the space of their power spectral densities, the geometric structure is achieved. Based on the general construction, for an example, whose power spectral density is obtained by use of the normalized Mexican hat wavelet, we show its information geometric structures, e.g., the dual connections, the curvaturesthe geodesics. Furthermore, the instability of the geodesic spreads on this manifold is analyzed via the behaviors of the length between two neighboring geodesics, the average volume element as well as the divergence (or instability) of the Jacobi vector field. Finally, the Lyapunov exponent is obtained.

本文言語English
論文番号123305
ジャーナルJournal of Mathematical Physics
53
12
DOI
出版ステータスPublished - 2012 12月 19
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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