Related papers: On Estimation of Hurst Scaling Exponent through Di…
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
In a recent work Manimaran et al. [Manimaran et al., Phys. Rev. E 72, 046120 (2005)] propose to use multiresolution Daubechies (DB) wavelets to (detrend) remove the low frequency trends and subsequently to quantify the multifractal…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative self-energy which contains all information about…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
For wall turbulence, moments of velocity fluctuations are known to be logarithmic functions of the height from the wall. This logarithmic scaling is due to the existence of a characteristic velocity and to the nonexistence of any…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that…
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the…
We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply…
In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
Under the basic assumption that the observed turbulent motions in molecular clouds are Alfvenic waves or turbulence, we emphasize that the Doppler broadening of molecular line profiles directly measures the velocity amplitudes of the waves…
We have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise, sinusoidal, square on the floating potential fluctuations acquired under different pressures in a DC…
We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent…