Relative entropy and large deviations under sublinear expectations

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.     

独立不同分布经验过程的大偏差原理

设（Xn) n≥1是取值于可测空间（E,B^A)的一串独立随机变量,考虑经验过程Ln(f)=1/n ∑i=1^nf(Xi),f属于某个有界函数集F。运用Talagrand-Ledoux偏差不等式,我们得到其大偏差估计的充分必要条件。最后推广到无界函数族情形。     

经验过程大偏差

本文研究了独立但不同分布的随机变量序列的经验过程大偏差原理.运用Talagrand-Ledoux偏差不等式建立了该经验过程大偏差估计的充分和必要条件.     

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.     

独立重尾随机变量随机和的大偏差估计

本文研究了一类独立重尾随机变量随机和S（t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率，其中{N(t),t≥0}是一放大晨负整数值随机变量；{Xn,n≥1}是非负，独立随机变量序列，并与{N(t),t≥０}独立。本文的结果将{Xn,n≥１}为独立同分布情形推广到了独立不同分布情形。     

关于有限马氏链相对熵密度和随机条件熵的一类极限定理

本文引进有限非齐次马链随机条件熵的概念，研究这个概念与相对熵密度的关系，并通过数列的绝对平均收敛的概念给出了有限非齐次马氏链的相对频率，相对熵密度和平均随机条件熵ａ．ｅ收敛于常数及有限非齐次马氏链熵率存在的条件。     

分数OU模型参数估计的大偏差

本文考虑了分数OU模型参数估计的大偏差,通过Laplace变换的技巧,得到了极大似然估计的大偏差.     

关于样本熵的一类强偏差定理

设{Xn,n≥1}是在可数集S中取值的一列随机变量,其联合分布为gn(x1,……,xn),pk(xk)是Xk的边缘分布。本文利用关于乘积分布∏^nk=1pk(xk)的相对熵和样本相对熵率的概念建立了关于参考样本熵的一类强偏差定理。     

LARGE DEVIATIONS FOR STATIONARY φ-MIXING SEQUENCES IN τ-TOPOLOGY

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.     

MODERATE DEVIATIONS AND LARGE DEVIATIONS 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） ｜.     

矩阵值Ornstein-Uhlenbeck过程的大偏差上界

本文研究了矩阵值Ornstein-Uhlenbeck过程的大偏差问题.通过构造指数鞅,得到了矩阵值Ornstein-Uhlenbeck过程的经验谱过程的大偏差上界,推广了厄米特布朗运动相应的结果.     

Upper Large Deviations for Mixing Random Sequence

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.     

Large deviations for empirical measures of switching diffusion processes with small parameters

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.     

集值测度的弱Radon—Nikodym导数及弱集值随机变量条件期望的存在性

讨论了集值工存在弱Radon-Nikodym导数的充要条件,对弱紧凸集值随机变量给出了其条件期望存在时的一个特征。     

可列齐次马氏链熵率的指数收敛速度

运用Markov不等式和期望、强遍历、δ系数的性质,利用Chang提出的研究指数收敛速度的方法,在给出5个引理的基础上,研究了初始状态给定的一类可列齐次马氏链熵率的收敛速度,推广了Chang的结果.     

PERTURBING FAMILIES OF GENERALIZED LYAPUNOV FUNCTIONS AND RELATIVE STABILITY IN TERMS OF TWO MEASURES

ＰＥＲＴＵＲＢＩＮＧＦＡＭＩＬＩＥＳＯＦＧＥＮＥＲＡＬＩＺＥＤＬＹＡＰＵＮＯＶ　ＦＵＮＣＴＩＯＮＳＡＮＤＲＥＬＡＴＩＶＥＳＴＡＢＩＬＩＴＹＩＮＴＥＲＭＳＯＦＴＷＯ　ＭＥＡＳＵＲＥＳＳｈａｎｇＬｉｊｕｎ（商立军）（ＴｈｅＦｏｕｒｔｈＭｉｌｉｔａｒｙＭｅ...     

分数布朗运动随机微分方程的MLE和Bayes估计的大偏差不等式

本文研究了分数布朗运动随机微分方程未知参数的极大似然估计和Bayes估计的偏差不等式.在一定的正则条件下.利用似然方法给出了这两个估计量的大偏差不等式.     

Large Deviations Rate Function for Polling Systems

In this paper, we identify the local rate function governing the sample path large deviation principle for a rescaled process n ^–1 Q _nt , where Q _t represents the joint number of clients at time t in a polling system with N nodes, one server and Markovian routing. By the way, the large deviation principle is proved and the rate function is shown to have the form conjectured by Dupuis and Ellis. We introduce a so called empirical generator consisting of Q _t and of two empirical measures associated with S _t , the position of the server at time t. One of the main step is to derive large deviations bounds for a localized version of the empirical generator. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program. The method seems to have a wide range of application including the famous Jackson networks, as shown at the end of this study. An example illustrates how this technique can be used to estimate stationary probability decay rate.