相关论文: Dynamical Reduction Models with General Gaussian N…
This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…
We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the…
The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises.…
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic case and as far as we work in $L^2$, the…
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…
In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…
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,…
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…
We are dealing with the Navier-Stokes equation in a bounded regular domain $D$ of $\mathbb{R}^2$, perturbed by an additive Gaussian noise $\partial w^{Q_\delta}/\partial t$, which is white in time and colored in space. We assume that the…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…
We show analytically that a linear transmitter with correlated Gaussian white noises displays a stochastic resonance. We discuss the relation of this problem to a generalized noisy logistic equation.
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…
In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…