Explanipedia

Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits Open

Benjamin Gess, Zhengyan Wu, Rangrang Zhang · 2024

Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint s…

McKean-Vlasov PDE with Irregular Drift and Applications to Large Deviations for Conservative SPDEs Open

Zhengyan Wu, Rangrang Zhang · 2022

Inspired by [Fehrman, Gess; Invent. Math., 2023], we provide a fine analysis of the McKean-Vlasov PDE with singular interactions and drift terms of square root form. As the corresponding skeleton equation of Dean-Kawasaki equation with sin…

Dean-Kawasaki Equation with Singular Interactions and Applications to Dynamical Ising-Kac Model Open

Likun Wang, Zhengyan Wu, Rangrang Zhang · 2022

Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correlated noise which can be viewed as fluctuating mean-field lim…

Central limit theorem and moderate deviation principle for stochastic scalar conservation laws Open

Zhengyan Wu, Rangrang Zhang · 2022

Central Limit Theorem And Moderate Deviation Principle For Inviscid Stochastic Burgers Equation Open

Zhengyan Wu, Rangrang Zhang · 2021

We establish a central limit theorem and prove a moderate deviation principle for inviscid stochastic Burgers equation. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and dou…

Quadratic Transportation Cost Inequality For Scalar Stochastic Conservation Laws Open

Rangrang Zhang, Tusheng Zhang · 2020

In this paper, we established a quadratic transportation cost inequality for scalar stochastic conservation laws driven by multiplicative noise. The doubling variables method plays an important role.

Ergodicity for stochastic conservation laws with multiplicative noise Open

Zhao Dong, Rangrang Zhang, Tusheng Zhang · 2020

We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in t…

Large deviations for stochastic porous media equations Open

Rangrang Zhang · 2020

In this paper, we establish the Freidlin-Wentzell type large deviation principles for porous medium-type equations perturbed by small multiplicative noise. The porous medium operator $Δ(|u|^{m-1}u)$ is allowed. Our proof is based on weak c…

Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noiss Open

Xuhui Peng, Jianhua Huang, Rangrang Zhang · 2020

In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main chall…

Large deviations for stochastic porous media equations Open

Rangrang Zhang · 2020

In this paper, we establish the Freidlin-Wentzell type large deviation principle for porous medium-type equations perturbed by small multiplicative noise. The porous medium operator $\\Delta (|u|^{m-1}u)$ is allowed. Our proof is based on …

Approximations of stochastic 3D tamed Navier-Stokes equations Open

Xuhui Peng, Rangrang Zhang · 2020

In this paper, we are concerned with 3D tamed Navier-Stokes equations with periodic boundary conditions, which can be viewed as an approximation of the classical 3D Navier-Stokes equations. We show that the strong solution of 3D tamed Navi…

On the small time asymptotics of quasilinear parabolic stochastic partial differential equations Open

Rangrang Zhang · 2019

In this paper, we establish a small time large deviation principles for the quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone.

On the small time asymptotics of scalar stochastic conservation laws Open

Zhao Yang Dong, Rangrang Zhang · 2019

In this paper, we establish a small time large deviation principles for scalar stochastic conservation laws driven by multiplicative noise. The doubling of variables method plays a key role.

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

Rangrang Zhang, Jie Xiong · 2019

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 …

Ergodicity for a class of semilinear stochastic partial differential equations Open

Zhao Dong, Rangrang Zhang · 2018

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…

3D tamed Navier-Stokes equations driven by multiplicative Lévy noise: Existence, uniqueness and large deviations Open

Zhao Dong, Rangrang Zhang · 2018

In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…

Harnack inequalities for a class of semilinear stochastic partial differential equations Open

Rangrang Zhang · 2018

In this article, we study a class of semilinear stochastic partial differential equations driven by an additive space time white noise. We establish Harnack inequalities for the semigroup associated with the solution by using coupling meth…

On the small‐time asymptotics of 3D stochastic primitive equations Open

Zhao Dong, Rangrang Zhang · 2018

In this paper, we establish a small‐time large deviation principle for the strong solution of three‐dimensional stochastic primitive equations driven by multiplicative noise, which involves not only the study of small noise but also the ch…

Large deviation principles for first-order scalar conservation laws with stochastic forcing Open

Zhao Dong, Jiang-Lun Wu, Rangrang Zhang, Tusheng Zhang · 2018

In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kin…

Large deviations for nematic liquid crystals driven by pure jump noise Open

Rangrang Zhang, Guoli Zhou · 2018

In this paper, we establish a large deviation principle for a stochastic evolution equation, which describes the system governing the nematic liquid crystals driven by pure jump noise. The proof is based on the weak convergence approach.

The asymptotic behavior of primitive equations with multiplicative noise Open

Rangrang Zhang, Guoli Zhou · 2018

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 …

Splitting up method for 2D stochastic primitive equations with multiplicative noise Open

Xuhui Peng, Rangrang Zhang · 2017

This paper concerns the convergence of an iterative scheme for 2D stochastic primitive equations on a bounded domain. The stochastic system is split into two equations: a deterministic 2D primitive equations with random initial value and a…

Large deviations for quasilinear parabolic stochastic partial differential equations Open

Zhao Dong, Rangrang Zhang, Tusheng Zhang · 2017

In this paper, we establish the Freidlin-Wentzell's large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The proof is based on the …

Exponential Mixing for SDEs under the total variation Open

Xuhui Peng, Rangrang Zhang · 2017

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…

A moderate deviation principle for 2D stochastic primitive equations Open

Rangrang Zhang, Guoli Zhou · 2017

In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach.

Markov selection and W-strong Feller for 3D stochastic primitive equations Open

Zhao Dong, Rangrang Zhang · 2017

Large deviation principles for 3D stochastic primitive equations Open

Zhao Dong, Jianliang Zhai, Rangrang Zhang · 2016

In this paper, we establish the large deviation principle for 3D stochastic primitive equations with small perturbation multiplicative noise. The proof is mainly based on the weak convergence approach.

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

Zhao Dong, Rangrang Zhang · 2015

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…

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