Information geometric characterization of the complexity of fractional Brownian motions

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 spectra...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2012-12, Vol.53 (12), p.1
Main Authors: Peng, Linyu, Sun, Huafei, Xu, Guoquan
Format: Article
Language:English
Subjects:
Brownian motion
Complexity
Curvature
Density
Exact sciences and technology
Geodetics
Geometry
Instability
Mathematical analysis
Mathematical functions
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
Spectra
Spectrum analysis
Stability
Topological manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 curvatures, and the 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4770047