Levels of complexity in scale-invariant neural signals

PC Ivanov, QDY Ma, RP Bartsch, JM Hausdorff… - Physical Review E …, 2009‏ - APS
Many physical and physiological signals exhibit complex scale-invariant features
characterized by 1/f scaling and long-range power-law correlations, indicating a possibly …

Simulation methods for linear fractional stable motion and FARIMA using the Fast Fourier Transform

S Stoev, MS Taqqu - Fractals, 2004‏ - World Scientific
We present efficient methods for simulation, using the Fast Fourier Transform (FFT)
algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely,(i) …

Fractional Lévy stable motion can model subdiffusive dynamics

K Burnecki, A Weron - Physical Review E—Statistical, Nonlinear, and Soft …, 2010‏ - APS
We show in this paper that the sample (time average) mean-squared displacement (MSD) of
the fractional Lévy α-stable motion behaves very differently from the corresponding …

On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic

S Stoev, MS Taqqu, C Park, JS Marron - Computer Networks, 2005‏ - Elsevier
The fluctuations of Internet traffic possess an intricate structure which cannot be simply
explained by long-range dependence and self-similarity. In this work, we explore the use of …

LASS: a tool for the local analysis of self-similarity

S Stoev, MS Taqqu, C Park, G Michailidis… - Computational statistics & …, 2006‏ - Elsevier
The Hurst parameter H characterizes the degree of long-range dependence (and asymptotic
self-similarity) in stationary time series. Many methods have been developed for the …

Multiscale aspects of cardiac control

PC Ivanov, Z Chen, K Hu, HE Stanley - Physica A: Statistical Mechanics …, 2004‏ - Elsevier
We report some recent attempts to understand the dynamics of complex physiologic
fluctuations by adapting and extending concepts and methods developed very recently in …

Wavelet estimation for operator fractional Brownian motion

P Abry, G Didier - 2018‏ - projecteuclid.org
Supplement to “Wavelet estimation for operator fractional Brownian motion”. In Section B of
the supplementary file Abry and Didier [2], we provide several additional auxiliary results …

Time-dependent scaling patterns in high frequency financial data

N Nava, T Di Matteo, T Aste - The European Physical Journal Special …, 2016‏ - Springer
We measure the influence of different time-scales on the intraday dynamics of financial
markets. This is obtained by decomposing financial time series into simple oscillations …

An overview of fractional order signal processing (FOSP) techniques

YQ Chen, R Sun, A Zhou - … and Information in …, 2007‏ - asmedigitalcollection.asme.org
This paper presents a brief overview of some existing fractional order signal processing
(FOSP) techniques where the developments in the mathematical communities are …

Irregularities and scaling in signal and image processing: multifractal analysis

P Abry, S Jaffard, H Wendt - Benoit Mandelbrot: a life in many …, 2015‏ - World Scientific
B. Mandelbrot gave a new birth to the notions of scale invariance, self-similarity and non-
integer dimensions, gathering them as the founding corner-stones used to build up fractal …