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

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on…

This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…

We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…

This paper is concerned with the existence of invariant measure for 3D stochastic primitive equations driven by linear multiplicative noise under non-periodic boundary conditions. The common method is to apply Sobolev imbedding theorem to…

We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…

This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…

In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…

We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…

In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role.

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.

In this paper, we study the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ for general parameter $\alpha\in(0,1)$ and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise…

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…

Central limit theorems and asymptotic properties of the minimum-contrast estimators of the drift parameter in linear stochastic evolution equations driven by fractional Brownian motion are studied. Both singular ($H < \frac{1}{2})$ and…

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps…