1,204 research outputs found
Stochastic models which separate fractal dimension and Hurst effect
Fractal behavior and long-range dependence have been observed in an
astonishing number of physical systems. Either phenomenon has been modeled by
self-similar random functions, thereby implying a linear relationship between
fractal dimension, a measure of roughness, and Hurst coefficient, a measure of
long-memory dependence. This letter introduces simple stochastic models which
allow for any combination of fractal dimension and Hurst exponent. We
synthesize images from these models, with arbitrary fractal properties and
power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure
Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure
Two types of Gaussian processes, namely the Gaussian field with generalized
Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy
covariance (GSGCC) are considered. Some of the basic properties and the
asymptotic properties of the spectral densities of these random fields are
studied. The associated self-similar random fields obtained by applying the
Lamperti transformation to GFGCC and GSGCC are studied.Comment: 32 pages, 6 figure
Measuring capital market efficiency: Long-term memory, fractal dimension and approximate entropy
We utilize long-term memory, fractal dimension and approximate entropy as
input variables for the Efficiency Index [Kristoufek & Vosvrda (2013), Physica
A 392]. This way, we are able to comment on stock market efficiency after
controlling for different types of inefficiencies. Applying the methodology on
38 stock market indices across the world, we find that the most efficient
markets are situated in the Eurozone (the Netherlands, France and Germany) and
the least efficient ones in the Latin America (Venezuela and Chile).Comment: 12 pages, 1 figure, 4 table
Earthquake statistics and fractal faults
We introduce a Self-affine Asperity Model (SAM) for the seismicity that
mimics the fault friction by means of two fractional Brownian profiles (fBm)
that slide one over the other. An earthquake occurs when there is an overlap of
the two profiles representing the two fault faces and its energy is assumed
proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law
with an exponent related to the roughness index of the profiles. Apart
from being analytically treatable, the model exhibits a non-trivial clustering
in the spatio-temporal distribution of epicenters that strongly resembles the
experimentally observed one. A generalized and more realistic version of the
model exhibits the Omori scaling for the distribution of the aftershocks. The
SAM lies in a different perspective with respect to usual models for
seismicity. In this case, in fact, the critical behaviour is not Self-Organized
but stems from the fractal geometry of the faults, which, on its turn, is
supposed to arise as a consequence of geological processes on very long time
scales with respect to the seismic dynamics. The explicit introduction of the
fault geometry, as an active element of this complex phenomenology, represents
the real novelty of our approach.Comment: 40 pages (Tex file plus 8 postscript figures), LaTeX, submitted to
Phys. Rev.
- …