Moderate Deviations for Stochastic Fractional Heat Equation Driven by Fractional Noise

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.

Download Full-text

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

Stochastics and Dynamics ◽

10.1142/s0219493716500222 ◽

2016 ◽

Vol 16 (06) ◽

pp. 1650022 ◽

Cited By ~ 4

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.

Download Full-text

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

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2018.10.025 ◽

2019 ◽

Vol 77 (4) ◽

pp. 928-946 ◽

Cited By ~ 2

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

Download Full-text

Central limit theorem and moderate deviation principle for CKLS model with small random perturbation

Statistics & Probability Letters ◽

10.1016/j.spl.2014.11.017 ◽

2015 ◽

Vol 98 ◽

pp. 6-11 ◽

Cited By ~ 4

Author(s):

Yujie Cai ◽

Shaochen Wang

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Random Perturbation ◽

Moderate Deviation ◽

Moderate Deviation Principle ◽

Deviation Principle ◽

Small Random Perturbation

Download Full-text

Quantitative normal approximations for the stochastic fractional heat equation

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-021-00198-7 ◽

2021 ◽

Author(s):

Obayda Assaad ◽

David Nualart ◽

Ciprian A. Tudor ◽

Lauri Viitasaari

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Heat Equation ◽

Central Limit ◽

Fractional Laplacian ◽

Spatial Average ◽

Spatial Covariance ◽

Fractional Heat Equation ◽

Variation Distance ◽

Functional Central Limit

AbstractIn this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space–time white noise and the white-colored noise with spatial covariance given by the Riesz kernel or a bounded integrable function. We show that the spatial average over a ball of radius R converges, as R tends to infinity, after suitable renormalization, towards a Gaussian limit in the total variation distance. We also provide a functional central limit theorem. As such, we extend recently proved similar results for stochastic heat equation to the case of the fractional Laplacian and to the case of general noise.

Download Full-text

A central limit theorem and moderate deviation principle for the stochastic 2D Oldroyd model of order one

Stochastic Partial Differential Equations Analysis and Computations ◽

10.1007/s40072-020-00176-5 ◽

2020 ◽

Author(s):

Manil T. Mohan

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Moderate Deviation ◽

Moderate Deviation Principle ◽

Oldroyd Model ◽

Deviation Principle

Download Full-text

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

Stochastics and Dynamics ◽

10.1142/s0219493720500173 ◽

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.

Download Full-text

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

Journal of Applied Probability ◽

10.1017/s0021900200022075 ◽

2002 ◽

Vol 39 (04) ◽

pp. 829-838 ◽

Cited By ~ 1

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).

Download Full-text