Related papers: Stochastic nonlinear differential equation generat…
1/f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
We consider a nonlinear stochastic heat equation in spatial dimension $d=2$, forced by a white-in-time multiplicative Gaussian noise with spatial correlation length $\varepsilon>0$ but divided by a factor of $\sqrt{\log\varepsilon^{-1}}$.…
1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic…
The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…
In an earlier work [P. J. Bardroff and S. Stenholm], we have derived a fully quantum mechanical description of excess noise in strongly damped lasers. This theory is used here to derive the corresponding quantum Langevin equations. Taking…
We consider a stochastic partial differential equation (SPDE) on a lattice \partial_t X=(\Delta-m^2)X-\lambda X^p+\eta where $\eta$ is a space-time L\'evy noise. A perturbative (in the sense of formal power series) strong solution is given…
We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…
Machine learning of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical differentiation is ill-posed to noise data, noise has become…
It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model under the only assumption that the emitter excitation and…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
For the stochastic partial differential equation $\frac{\partial u}{\partial t}=\mathcal L u +u\dot W$ where $\dot W$ is Gaussian noise colored in time and $\mathcal L$ is the infinitesimal generator of a Feller process $X$, we obtain…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
Based on analyzing various physical examples for 1/f noise we found that the 1/f noise is caused by generating conditions as resonance in acoustics and the effect of matter carrier is secondary. All the physical reasons are summarized into…