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

2019 ◽  
Vol 77 (4) ◽  
pp. 928-946 ◽  
Author(s):  
Rangrang Zhang ◽  
Guoli Zhou ◽  
Boling Guo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Moderate Deviation ◽  
Primitive Equations ◽  
Moderate Deviation Principle ◽  
Deviation Principle

Moderate deviations for fourth-order stochastic heat equations with fractional noises

2016 ◽  
Vol 16 (06) ◽  
pp. 1650022 ◽  
Author(s):  
Juan Yang ◽  
Yiming Jiang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Moderate Deviation ◽  
Heat Equations ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Stochastic Heat Equations ◽  
Fractional Noises

In this paper, we obtain a central limit theorem and prove a moderate deviation principle for fourth-order stochastic heat equations with fractional noises.

scholarly journals Moderate Deviations for Stochastic Fractional Heat Equation Driven by Fractional Noise

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Xichao Sun ◽  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Heat Equation ◽  
Central Limit ◽  
Moderate Deviation ◽  
Heat Equations ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Deviation Principle ◽  
Fractional Noises

We consider a class of stochastic fractional heat equations driven by fractional noises. A central limit theorem is given, and a moderate deviation principle is established.

Central limit theorem and moderate deviations for a perturbed stochastic Cahn–Hilliard equation

2019 ◽  
Vol 20 (03) ◽  
pp. 2050017
Author(s):  
Ruinan Li ◽  
Xinyu Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
White Noise ◽  
Central Limit ◽  
Moderate Deviation ◽  
Hilliard Equation ◽  
Deviation Principle ◽  
Cahn Hilliard Equation ◽  
Weak Convergence Approach

In this paper, we prove a central limit theorem and a moderate deviation principle for a perturbed stochastic Cahn–Hilliard equation defined on [Formula: see text] with [Formula: see text]. This equation is driven by a space-time white noise. The weak convergence approach plays an important role.

Moderate deviation for super-Brownian Motion with super-Brownian immigration

2002 ◽  
Vol 39 (04) ◽  
pp. 829-838 ◽  
Author(s):  
Wen-Ming Hong
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Large Deviation ◽  
Moderate Deviation ◽  
The Central Limit Theorem ◽  
Large Deviation Principles ◽  
Super Brownian Motion ◽  
Random Immigration

Moderate deviation principles are established in dimensionsd≥ 3 for super-Brownian motion with random immigration, where the immigration rate is governed by the trajectory of another super-Brownian motion. It fills in the gap between the central limit theorem and large deviation principles for this model which were obtained by Hong and Li (1999) and Hong (2001).

Functional central limit theorems and moderate deviations for Poisson cluster processes

2020 ◽  
Vol 52 (3) ◽  
pp. 916-941
Author(s):  
Fuqing Gao ◽  
Yujing Wang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Maximal Inequality ◽  
Moderate Deviation ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Poisson Cluster ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit ◽  
Cluster Processes

AbstractIn this paper, we consider functional limit theorems for Poisson cluster processes. We first present a maximal inequality for Poisson cluster processes. Then we establish a functional central limit theorem under the second moment and a functional moderate deviation principle under the Cramér condition for Poisson cluster processes. We apply these results to obtain a functional moderate deviation principle for linear Hawkes processes.

Gaussian Approximation via Martingale Methods

2019 ◽  
pp. 95-144
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Functional Form ◽  
Gaussian Approximation ◽  
Moderate Deviation ◽  
Stationary Sequences ◽  
Moderate Deviations Principle ◽  
The Central Limit Theorem ◽  
Projective Type

Gordin’s seminal paper (1969) initiated a line of research in which limit theorems for stationary sequences are proved via appropriate approximations by stationary martingale difference sequences followed by an application of the corresponding limit theorem for such sequences. In this chapter, we first review different ways to get suitable martingale approximations and then derive the central limit theorem and its functional form for strictly stationary sequences under various types of projective criteria. More general normalizations than the traditional ones will be also investigated, as well as the functional moderate deviation principle. We shall also address the question of the functional form of the central limit theorem for not necessarily stationary sequences. The last part of this chapter is dedicated to the moderate deviations principle and its functional form for stationary sequences of bounded random variables satisfying projective-type conditions.

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