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Rangrang Zhang

Publications and source records attributed to Rangrang Zhang.

29 records · Page 2Linked to original sources
arXiv2019

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

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.

math.PR↗
arXiv2018

Exponential Mixing for 3D Stochastic Primitive Equations

In this paper, we prove that weak solutions of 3D stochastic primitive equations have exponential mixing property if the noise is sufficiently smooth and non-degenerate. With the help of uniqueness of strong solution of 3D stochastic primitive equations, we obtain that all weak solutions which are limitations of Galerkin approximations share the same invariant measure. In particular, the invariant measure of strong solution is unique. The coupling method plays a key role.

math.PR↗
arXiv2018

Ergodicity for a class of semilinear stochastic partial differential equations

In this paper, we establish the existence and uniqueness of invariant measures for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to SPDEs of various types such as the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise.

math.PR↗
arXiv2018

On the small time asymptotics of 3D stochastic primitive equations

In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.

math.PR↗
arXiv2018

Exponential Mixing for SDEs under the total variation

First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic results on $\mR^d$ require that the process is irreducible, we weaken it to some weak form of irreducibility in this article. The main method used in this article is coupling. Then, we apply our abstract ergodic result to stochastic differential equations driven by a Lévy noise and obtain a new result.

math.PR↗
arXiv2018

The asymptotic behavior of primitive equations with multiplicative noise

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 proving the tightness of the distribution of the solution. However, this method fails because of the non-linearity and non-periodic boundary conditions of the stochastic primitive equations. To overcome the difficulties, we show the existence of random attractor by proving the compact property and the regularity of the solution operator. Then we show the existence of invariant measure.

math.PR↗
arXiv2016

Markov Selection and $W$-strong Feller for 3D Stochastic Primitive Equations

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.

math.PR↗
arXiv2016

Long-time behavior of 3D Stochastic Planetary Geostrophic Viscous Model

This paper reports the 3D planetary geostrophic viscous model has the exponential ergodicity and global attractor if this model is driven by an additive random noise, which results in the support of the integration of invariant measure for the dynamic is exactly a minimal global attractor. It's worth mentioning that this global attractor has finite Hausdorff dimension.

math.PR↗