Related papers: 1/f noise from nonlinear stochastic differential e…
Decoherence induced by the laser frequency noise is one of the most important obstacles in the quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet…
Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the discovery problem. Recently, the discovery of traditional ODEs dynamics using linear multistep methods…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
A chemical system consisting of two species, one of which evolves deterministically and independently of the other, which in turn is driven by the dynamics of the former and by an additional multiplicative Gaussian white noise, displays a…
We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…
We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which…
Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…
This report is aimed at reviving the explanation of flicker-noise observations as the result of spectral measurement of very low-frequency but stationary narrow-band fluctuations named as infralow-frequency noise (ILF noise) [A. Ya.…
Within the framework of stochastic electrodynamics we derive the noise spectrum of a laser beam reflected from a suspended mirror. The electromagnetic field follows Maxwell's equations and is described by a deterministic part that accounts…
We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar…
A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is…
In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation.…
We develop a method for estimating the shear power spectra from weak lensing observations and test it on simulated data. Our method describes the shear field in terms of angular power spectra and cross correlation of the two shear modes…
We calculate time correlation functions in the Bak-Sneppen model (Phys. Rev. Lett. {\bf 71} 4083 (1993)), a model showing self-organised criticality. For a random neighbour version of the model, analytical results are presented, while on a…
We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with…
The major goal of the present paper is to find out the manifestation of the boundedness of fluctuations. Two different subjects are considered: (i) an ergodic Markovian process associated with a new type of large scaled fluctuations at…