Related papers: Analysis of fractional Gaussian noises using level…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is…
I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristics is to be determined by the junction. This…
With the astrophysics community working towards the first observations and characterizations of Earth-like exoplanets, interest in space-based nulling interferometry has been renewed. This technique promises unique scientific and technical…
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…
Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate ("escape noise"). While input noise lends itself to modeling biophysical noise…
The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…
We discuss the link between uncorrelated noise and Hurst exponent for one and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose…
In a previous paper, we studied the ergodic properties of an Euler scheme of a stochastic differential equation with a Gaussian additive noise in order to approximate the stationary regime of such equation. We now consider the case of…
We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…
In this paper, we consider smooth shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the mean number of crossings function is obtained through an integral formula.…
Recently, score-based generative models have been successfully employed for the task of speech enhancement. A stochastic differential equation is used to model the iterative forward process, where at each step environmental noise and white…
Directed transport of overdamped Brownian particles driven by fractional Gaussian noises is investigated in asymmetrically periodic potentials. By using Langevin dynamics simulations, we find that rectified currents occur in the absence of…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
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…
Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for $1/f$ noise in solid-state quantum information…