Related papers: A moderate deviation principle for 2D stochastic p…

In this paper we consider the Lagrangian Averaged Navier-Stokes Equations, also known as, LANS-$\alpha$ Navier-Stokes model on the two dimensional torus. We assume that the noise is a cylindrical Wiener process and its coefficient is…

We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a…

The term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak…

Small noise problems are quite important for all types of stochastic differential equations. In this paper we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter H between 1/4 and 1/2.…

We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated…

We consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. We prove that a moderate deviation principle holds for all…

In this paper, we establish a large deviation principle for 2D stochastic Chemotaxis-Navier-Stokes equation perturbed by a small multiplicative noise. The main difficulties come from the lack of a suitable compact embedding into the space…

In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.

Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the…

By using the weak convergence method, we establish the large and moderate deviation principles for the multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients driven by L\'{e}vy noise in this paper. The Bihari's inequality is used to…

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and…

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…

We prove a central limit theorem characterizing the small noise fluctuations of stochastic PDEs of fluctuating hydrodynamics type. The results apply to the case of nonlinear and potentially degenerate diffusions and irregular noise…

In this paper, we establish a large deviation principle for a type of stochastic partial differential equations (SPDEs) with locally monotone coefficients driven by L\'evy noise. The weak convergence method plays an important role.

The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…

We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of…