LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.

MODERATE DEVIATIONS AND LARGEDE VIATIONS FOR A TEST OF SYMMETRY BASED ON KERNEL DENSITY ESTIMATOR

Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.

MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ORNSTEIN-UHLENBECK PROCESS

We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.

MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL

The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.

CENTRAL LIMIT THEOREM AND MODERATE DEVIATIONS FOR A CLASS OF SEMILINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.

MODERATE DEVIATIONS FOR THE BESSEL CLOCK

By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained.

Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

Moderate Deviations for Parameter Estimation in the Fractional Ornstein–Uhlenbeck Processes with Periodic Mean

In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.

Moderate Deviations for Random Sums of Heavy-Tailed Random Variables

Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.

Deviation inequalities for quadratic Wiener functionals and moderate deviations for parameter estimators

We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.

Moderate Deviations for M-estimators in Linear Models with φ-mixing Errors

In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary Ф-mixing sequence. The results are applied to study many different types of M-estimators such as Huber＇s estimator, L^P-regression estimator, least squares estimator and least absolute deviation estimator.

SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES

This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.

Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data

Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for {sup x∈sd-1 ｜fn（x） - E（fn（x））｜, n ≥ 1} hold.

Moderate Deviations for Stochastic Models of Two-Dimensional Second-Grade Fluids Driven by Lévy Noise

In this paper,we establish a moderate deviation principle for stochastic models of two-dimensional second-grade fluids driven by Lévy noise.We will adopt the weak convergence approach.Because of the appearance of jumps,this result is significantly different from that in Gaussian case.

Moderate deviations for neutral functional stochastic differential equations driven by Levy noises

Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.

Moderate Deviations for a Test of Symmetry Based on Deconvolution Kernel Density Estimators

Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n （ x ）to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R ｜ f n （ x ） f n（ x） ｜are given by Gine and Guillou＇s exponential inequality.

Convergence Rates for Probabilities of Moderate Deviations for Moving Average Processes

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.

Moderate Deviations for Marked Hawkes Processes

We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31,433-451 （2015）]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.