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.

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

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.

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