Related papers: On the White-Noise Limit of the Colored Linear Inv…
In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The Linear Inverse Model (LIM) is a class of data-driven methods that extract dynamic and stochastic…
The Linear Inverse Model (LIM) is a class of data-driven methods that construct approximate linear stochastic models to represent complex observational data. The stochastic forcing can be modeled using either Gaussian white noise or…
We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into…
We consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero. The work is motivated by an experiment…
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force…
We study the asymptotic behavior, uniform-in-time, of a non-linear dynamical system under the combined effects of fast periodic sampling with period $\delta$ and small white noise of size $\varepsilon,\thinspace 0<\varepsilon,\delta \ll 1$.…
The phenomenon of stochastic resonance, wherein the stimulus-response of a system can be maximized by an intermediate level of noise, has been extensively investigated through linear response theory. As yet a unified response-noise or…
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…
The concept of time-correlated noise is important to applied stochastic modelling. Nevertheless, there is no generally agreed-upon definition of the term red noise in continuous-time stochastic modelling settings. We present here a rigorous…
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…
We investigate the collective signal response of two typical nonlinear dynamical models, the mean-field coupled overdamped bistable oscillators and the underdamped Duffing oscillators, with respect to both the additive Ornstein-Uhlenbeck…
We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a…
Many phenomena in nature are described by excitable systems driven by colored noise. The temporal correlations in the fluctuations hinder an analytical treatment. We here present a general method of reduction to a white-noise system,…
The Stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex…
Instance- and Label-dependent label Noise (ILN) widely exists in real-world datasets but has been rarely studied. In this paper, we focus on Bounded Instance- and Label-dependent label Noise (BILN), a particular case of ILN where the label…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
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 recent study on the effect of colored driving noise on the escape from a metastable state derives an analytic expression of the transfer function of the leaky integrate-and-fire neuron model subject to colored noise. Here we present an…