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Peng, Linyu; Sun, Huafei; Xu, Guoquan

Information geometric characterization of the complexity of fractional Brownian motions. (English) Zbl 1293.60047

J. Math. Phys. 53, No. 12, 123305, 12 p. (2012).
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.{
©2012 American Institute of Physics}

Cited in 5 Documents

MSC:

60G22 Fractional processes, including fractional Brownian motion
94A17 Measures of information, entropy
53B21 Methods of local Riemannian geometry
53C22 Geodesics in global differential geometry
65C60 Computational problems in statistics (MSC2010)
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)

Keywords:

fractional Brownian motion; information geometry; dual connection; curvature; geodesic; Lyapunov exponent
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