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 devi...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.展开更多
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 mod...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） ｜.展开更多
We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
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 fo...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.展开更多
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-ide...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.展开更多
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...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.展开更多
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 expl...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.展开更多
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 deviati...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.展开更多
In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘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.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘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） ｜.
基金Research supported by the National Natural Science Foundation of China (10571139)
文摘We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
基金Supported by the National Natural Science Foundation of China (10271091)
文摘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.
基金supported by the Youth Foundation of Hubei Province Department of Education of China (Q200710002)
文摘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.
基金supported by NSFF(17BTJ034)The research of WANG was supported by NSFC(11871382,11771161).
文摘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.
基金Research supported by the National Natural Science Foundation of China(10871153)funded by the Revitalization Project of Zhongnan University of Economics and Law
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].
