Related papers: Large Deviations for the Stochastic Shell Model of…
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…
We consider a lattice gas on the discrete d-dimensional torus $(\mathbb{Z}/N\mathbb{Z})^d$ with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
We present an analytic and numerical analysis of the Gledzer-Ohkitani-Yamada (GOY) cascade model for turbulence. We concentrate on the dynamic correlations, and demonstrate both numerically and analytically, using resummed perturbation…
Whether turbulence intermittencies shall be described by a log-Poisson, a log-stable pdf or other distributions is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk and random vortex stretching is…
This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…
In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…
In this paper, we find a new large scale instability displayed by a rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic…
We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…
This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…
It has been shown recently that intermittency of the Gledzer Ohkitani Yamada (GOY) shell model of turbulence has to be related to singular structures whose dynamics in the inertial range includes interactions with a background of…
In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative $L\acute{e}vy$ noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in…
We introduce a stochastic version of Proudman-Taylor model, a 2D-3C fluid approximation of the 3D Navier-Stokes equations, with the small-scale turbulence modeled by a transport-stretching noise. For this model we may rigorously take a…
We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The…
In this article, we established a large deviation principle for invariant measures of solutions of stochastic partial differential equations with two reflecting walls driven by space-time white noise.
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…