相关论文: Cyclic fractional Gaussian noise: time and frequen…
Fractional Gaussian noise (fGn) is a self-similar stochastic process used to model anti-persistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst…
Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the…
Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhibits a property of power-like decaying autocorrelation…
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a…
Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and…
This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new…
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the…
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…
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian.…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
Current fluctuations play an important role in non-equilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations…
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise in a superharmonic external potential of the form $U(x)\propto x^{2n}$ ($n\in\mathbb{N}$). When the noise is considered to be external,…
Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here,…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
The goal of this paper is to propose a new approach to asymptotic analysis of the finite predictor for stationary sequences. It produces the exact asymptotics of the relative prediction error and the partial correlation coefficients. The…
We discuss a family of random fields indexed by a parameter $s\in \mathbb{R}$ which we call the fractional Gaussian fields, given by \[ \mathrm{FGF}_s(\mathbb{R}^d)=(-\Delta)^{-s/2} W, \] where $W$ is a white noise on $\mathbb{R}^d$ and…
We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional…
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in particular, we obtain recurrence relations for them. We also make…