In this paper, we consider the stochastic Burgers' equation, which is forced by multiplicative noise in the Stratonovich sense. To get a new trigonometric and hyperbolic stochastic solutions, we ap...

The effect of multiplicative noise on the exact solutions of the stochastic Burgers' equation

In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise. In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system. Furthermore, the SPDEs correctly simulate the rare events in the particle process. We prove that the solutions satisfy a zero-noise large deviations principle with rate function equal to the rate function describing the deviations of the symmetric simple exclusion process from its hydrodynamic limit.

Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

This work is concerned about some asymptotic behaviour of the two-dimensional stochastic convective Brinkman–Forchheimer (SCBF) equations, which describes the motion of incompressible viscous fluid...

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to stochastic partial differential equations of various types such as the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise.

Semilinear stochastic partial differential equations: central limit theorem and moderate deviations

Global well-posedness of stochastic 2D primitive equations with random initial conditions

In this paper, we establish a central limit theorem and a moderate deviation for two-dimensional stochastic primitive equations driven by multiplicative noise. This is the first result about the limit theorem and the moderate deviations for stochastic primitive equations. The proof of the results relies on the weak convergence method and some delicate and careful a p r i o r i estimates.

Stochastic 2D primitive equations: Central limit theorem and moderate deviation principle

In this paper, we study the stochastic vector-valued Burgers equations with non-periodic boundary conditions. We first apply a contraction principle argument to show local existence and uniqueness of a mild solution to this model. Then, toward obtaining the global well-posedness, we derive a priori estimates of the local solution by utilizing the maximum principle. Finally, we establish, by means of the weak convergence approach, the Freidlin–Wentzell type large deviation principle for 3D stochastic Burgers equations when the noise term goes to zero.

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Rangrang Zhang

Papers

Stochastic 2D primitive equations: Central limit theorem and moderate deviation principle

Global well-posedness and large deviations for 3D stochastic Burgers equations