Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics

2021 ◽  
Vol 133 ◽  
pp. 74-110
Author(s):  
Arnab Ganguly ◽  
P. Sundar
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Moderate Deviation ◽  
Invariant Distributions ◽  
Ergodic Diffusions

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).

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.

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.

Limit theorems for a supercritical Poisson random indexed branching process

2016 ◽  
Vol 53 (1) ◽  
pp. 307-314 ◽  
Author(s):  
Zhenlong Gao ◽  
Yanhua Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Central Limit ◽  
Limit Theorems ◽  
Branching Process ◽  
Law Of Large Numbers ◽  
Moderate Deviation ◽  
Large Numbers

Abstract Let {Zn, n = 0, 1, 2, . . .} be a supercritical branching process, {Nt, t ≥ 0} be a Poisson process independent of {Zn, n = 0, 1, 2, . . .}, then {ZNt, t ≥ 0} is a supercritical Poisson random indexed branching process. We show a law of large numbers, central limit theorem, and large and moderate deviation principles for log ZNt.

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

2002 ◽  
Vol 39 (4) ◽  
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 dimensions d ≥ 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).

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.

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