Related papers: Spectral densities describing off-white noises
Low-frequency 1/f-noise occurs at all levels of the nature organization and became an actual factor of nanotechnologies, but in essence it remains misunderstood by its investigators. Here, once again it is pointed out that such the state of…
A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by It\^o stochastic differential equations. The stochastic differential equations derived for the…
The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables…
When the rate of shot noise is controlled by on-off states we speak of intermittent shot noise. The on-off states lead to alternately occurring clusters of events and intermissions, respectively. We derive the power spectrum of the…
Conditions are given, sufficient for the distribution of an Ornstein-Uhlenbeck process with L\'evy noise to be absolutely continuous or to possess a smooth density. For the processes with non-degenerate drift coefficient, these conditions…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
We consider the nonparametric estimation of the density function of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range…
In the framework of sublinear expectation, we have introduced a new type of G-Gaussian random fields, which contain a type of spatial white noise as a special case. Based on this result, we also have introduced a spatial-temporal G-white…
We formulate the stochastic dynamics of a particle subject to internal non-white (coloured) noise in terms of path-integrals. In the simplest case, where the noise is exponentially correlated, the weak-noise limit is characterised by…
The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past…
Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is…
We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1, contains the support of the white noise. Then, we prove local well-posedness in \hat{b}^s_{p,…
We present some analytic, non-perturbative results for the invariant density rho(x) for noisy one-dimensional maps at fully developed chaos. Under periodic boundary conditions, the Fourier expansion method is used to show precisely how…
Time-irreversibility is a distinctive feature of non-equilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical…
For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients, we find necessary and…
Basic aspects of the background of gravitational waves and its mathematical characterization are reviewed. The spectral energy density parameter $\Omega(f)$, commonly used as a quantifier of the background, is derived for an ensemble of…
We prove that if $\Om \subseteq \R^2$ is bounded and $\R^2 \setminus \Om$ satisfies suitable structural assumptions (for example it has a countable number of connected components), then $W^{1,2}(\Om)$ is dense in $W^{1,p}(\Om)$ for every…
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy…
Testing for multi-dimensional white noise is an important subject in statistical inference. Such test in the high-dimensional case becomes an open problem waiting to be solved, especially when the dimension of a time series is comparable to…
We study the influence of a fast noise on Landau-Zener transitions. We demonstrate that a fast colored noise much weaker than the conventional white noise can produce transitions itself or can change substantially the Landau-Zener…