Moderate deviations for linear eigenvalue statistics of β-ensembles

Random Matrices Theory and Application ◽

10.1142/s2010326322500174 ◽

2021 ◽

pp. 2250017

Author(s):

Fuqing Gao ◽

Jianyong Mu

Keyword(s):

Moderate Deviation ◽

Main Ingredient ◽

Moderate Deviation Principle ◽

Uniform Estimates ◽

Linear Eigenvalue Statistics ◽

Deviation Principle ◽

Eigenvalue Statistics ◽

Real Analytic ◽

The One ◽

Analytic Potential

We establish a moderate deviation principle for linear eigenvalue statistics of [Formula: see text]-ensembles in the one-cut regime with a real-analytic potential. The main ingredient is to obtain uniform estimates for the correlators of a family of perturbations of [Formula: see text]-ensembles using the loop equations.

Moderate deviation principle for multivalued stochastic differential equations

Stochastics and Dynamics ◽

10.1142/s021949372050015x ◽

2019 ◽

Vol 20 (03) ◽

pp. 2050015 ◽

Cited By ~ 1

Author(s):

Hua Zhang

Keyword(s):

Brownian Motion ◽

Weak Convergence ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Moderate Deviation ◽

Reflected Brownian Motion ◽

Moderate Deviation Principle ◽

Deviation Principle ◽

Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

Examples of moderate deviation principle for diffusion processes

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2006.6.803 ◽

2006 ◽

Vol 6 (4) ◽

pp. 803-828 ◽

Cited By ~ 21

Author(s):

A. Guillin ◽

◽

R. Liptser ◽

Keyword(s):

Diffusion Processes ◽

Moderate Deviation ◽

Moderate Deviation Principle ◽

Deviation Principle

ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964819000275 ◽

2019 ◽

Vol 34 (4) ◽

pp. 570-582

Author(s):

Yu Miao ◽

Huanhuan Ma ◽

Qinglong Yang

Keyword(s):

Law Of Large Numbers ◽

Moderate Deviation ◽

Bernoulli Model ◽

Strong Law ◽

Asymptotic Behaviors ◽

Moderate Deviation Principle ◽

Deviation Principle ◽

Large Numbers ◽

Bernoulli Variables ◽

Image Position

AbstractWe consider a class of correlated Bernoulli variables, which have the following form: for some 0 < p < 1, $$\begin{align}{P(X_{j+1}=1 \vert {\cal F}_{j})= (1-\theta_j)p+\theta_jS_j/j,}\end{align}$$where 0 ≤ θj ≤ 1, $S_n=\sum _{j=1}^nX_j$ and ${\cal F}_n=\sigma \{X_1,\ldots , X_n\}$. The aim of this paper is to establish the strong law of large numbers which extend some known results, and prove the moderate deviation principle for the correlated Bernoulli model.

Moderate deviation principle for Brownian motions on the unit sphere in

Statistics & Probability Letters ◽

10.1016/j.spl.2013.07.010 ◽

2013 ◽

Vol 83 (11) ◽

pp. 2486-2491

Author(s):

Lei Chen ◽

Fuqing Gao

Keyword(s):

Unit Sphere ◽

Moderate Deviation ◽

Brownian Motions ◽

Moderate Deviation Principle ◽

Deviation Principle

The moderate deviation principle for minimizers of convex processes

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.124202 ◽

2020 ◽

Vol 490 (1) ◽

pp. 124202

Author(s):

Mingzhi Mao ◽

Wenqiang Luo

Keyword(s):

Moderate Deviation ◽

Moderate Deviation Principle ◽

Convex Processes ◽

Deviation Principle

Asymptotic normality and moderate deviation principle for high-dimensional likelihood ratio statistic on block compound symmetry covariance structure

Statistics ◽

10.1080/02331888.2020.1715408 ◽

2020 ◽

Vol 54 (1) ◽

pp. 114-134

Author(s):

Gaoming Sun ◽

Junshan Xie

Keyword(s):

Asymptotic Normality ◽

Likelihood Ratio ◽

Likelihood Ratio Statistic ◽

Covariance Structure ◽

Moderate Deviation ◽

High Dimensional ◽

Moderate Deviation Principle ◽

Deviation Principle ◽

Compound Symmetry

Moderate deviation principle for maximum-likelihood estimator

Statistics ◽

10.1080/02331888.2013.822501 ◽

2013 ◽

Vol 48 (4) ◽

pp. 766-777 ◽

Cited By ~ 4

Author(s):

Yu Miao ◽

Yanling Wang

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Moderate Deviation ◽

Likelihood Estimator ◽

Moderate Deviation Principle ◽

Deviation Principle

Moderate deviation principle for m-dependent random variables*

Lithuanian Mathematical Journal ◽

10.1007/s10986-018-9382-7 ◽

2018 ◽

Vol 58 (1) ◽

pp. 54-68

Author(s):

Yu Miao ◽

Jianan Zhu ◽

Jianyong Mu

Keyword(s):

Random Variables ◽

Moderate Deviation ◽

Dependent Random Variables ◽

Moderate Deviation Principle ◽

Deviation Principle

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

Moderate deviation principle for $ m $-dependent random variables under the sub-linear expectation

AIMS Mathematics ◽

10.3934/math.2022331 ◽

2022 ◽

Vol 7 (4) ◽

pp. 5943-5956

Author(s):

Shuang Guo ◽

◽

Yong Zhang

Keyword(s):

Random Variables ◽

Moderate Deviation ◽

Dependent Random Variables ◽

Moderate Deviation Principle ◽

Deviation Principle ◽

Dependent Sequence ◽

Definition Of ◽

Independent Identically Distributed

<abstract><p>Let $ \{X_n, n\geq1\} $ be a sequence of $ m $-dependent strictly stationary random variables in a sub-linear expectation $ (\Omega, \mathcal{H}, \mathbb{E}) $. In this article, we give the definition of $ m $-dependent sequence of random variables under sub-linear expectation spaces taking values in $ \mathbb{R} $. Then we establish moderate deviation principle for this kind of sequence which is strictly stationary. The results in this paper generalize the result that in the case of independent identically distributed samples. It provides a basis to discuss the moderate deviation principle for other types of dependent sequences.</p></abstract>