相关论文: Anomalous Diffusion: Fractional Brownian Motion vs…
Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two…
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…
We discuss how to construct reliably well "a lattice and an integer time" version of a super-diffusive continuous-space and -time fractional Brownian motion (fBm) -- an experimentally-relevant non-Markovian Gaussian stochastic process with…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
The Wiener's path integral plays a central role in the studies of Brownian motion. Here we derive exact path-integral representations for the more general \emph{fractional} Brownian motion (fBm) and for its time derivative process -- the…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…
Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic…
Closed-form expressions, parametrized by the Hurst exponent $H$ and the length $n$ of a time series, are derived for paths of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) in the $\mathcal{A}-\mathcal{T}$ plane,…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…
We discuss the situations under which Brownian yet non-Gaussian (BnG) diffusion can be observed in the model of a particle's motion in a random landscape of diffusion coefficients slowly varying in space. Our conclusion is that such…
Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random…
Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance \[ R^{(H,K)}(s,t)= 2^{-K} \left( \left(|s|^{2H}+|t|^{2H} \right)^{K}-|t-s|^{2HK}\right), \qquad s,t\in R. \] We study the existence of bfBm for a given pair…
We report in this paper a thorough study on the the dynamical mechanics of the fractional Brownian motion systems. Where several non-trivial properties are revealed such as the abundant non-Markovian effects resulted from the fractional…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…
Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…
Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in (0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional Brownian motion in Brownian motion time (of index $H$), recently studied in…