Related papers: Tempered fractional Brownian motion: wavelet estim…
Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior…
A crossover from a non-Gaussian to Gaussian sub-diffusion has been observed ubiquitously in various polymeric/molecular glass-formers. We have developed a framework which generalizes the fractional Brownian motion (fBm) model to incorporate…
In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter $H>1/2.$ The Black-Scholes model for the values of returns of an asset using fBm is given as, [Y_t=Y_0…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter…
This paper reviews the formulation of the Feynman-Vernon model of linear dissipative systems for a standard Brownian particle moving in an external potential $V(x,t)$ and introduces the formulation of a generalized oscillator model of a…
In attempting to quantify statistically the density structure of the interstellar medium, astronomers have considered a variety of fractal models. Here we argue that, to properly characterise a fractal model, one needs to define precisely…
We construct fractional Brownian motion (fBm), sub-fractional Brownian motion (sub-fBm), negative sub-fractional Brownian motion (nsfBm) and the odd part of fBm in the sense of Dzhaparidze and van Zanten (2004) by means of limiting…
In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$.…
There is much confusion in the literature over Hurst exponent (H). The purpose of this paper is to illustrate the difference between fractional Brownian motion (fBm) on the one hand and Gaussian Markov processes where H is different to 1/2…
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown…
The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
Quantum turbulence is numerically studied by solving the Gross-Pitaevskii equation. Introducing both the energy dissipation at small scales and the energy injection at large scales, we succeed in obtaining the steady turbulence made by the…
Stratification can cause turbulence spectra to deviate from Kolmogorov's isotropic -5/3 power-law scaling in the universal equilibrium range at high Reynolds numbers. However, a consensus has not been reached with regard to the exact shape…
We perform a comparative study of applicability of the Multifractal Detrended Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method in proper detecting of mono- and multifractal character of data. We quantify…
The aim of this Short Note is to highlight that the {\it generalized grey Brownian motion} (ggBm) is an anomalous diffusion process driven by a fractional integral equation in the sense of Erd\'elyi-Kober, and for this reason here it is…
We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm)…