Information geometric characterization of the complexity of fractional Brownian motions

Linyu Peng, Huafei Sun, Guoquan Xu

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11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number123305
JournalJournal of Mathematical Physics
Volume53
Issue number12
DOIs
Publication statusPublished - 2012 Dec 19
Externally publishedYes

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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