Moderate deviations for linear eigenvalue statistics of β-ensembles

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

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
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.

ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

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 a class of stochastic partial differential equations

2016 ◽  
Vol 53 (1) ◽  
pp. 279-292 ◽  
Author(s):  
Parisa Fatheddin ◽  
Jie Xiong
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Moderate Deviation ◽  
Partial Differential ◽  
Moderate Deviation Principle ◽  
Lipschitz Continuous ◽  
Deviation Principle ◽  
Super Brownian Motion

Abstract We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two important population models: super-Brownian motion and the Fleming–Viot process.

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