GL-统计量的中偏差及大偏差

本文讨论GL-统计量的中偏差。Cramer型大偏差及 Chernoff型大偏差。其中关于GL-统计量的中偏差及Cramer 型大偏差结果推广了Vandemaele et al有关L-统计量,U-统计量的结果。这里,首次给出关于 U-统计量的 Chernoff型大偏差。应用它得到 GL-统计量的 Chernoff型的大偏差。所采用的方法为 Gateux微分逼近和 Bahadur 分位数表示法。     

上尾渐近独立随机变量和的大偏差的渐近下界(英文)

本文研究了多元风险模型中服从长尾分布的带上尾渐近独立的随机变量和的大偏差渐近下界.利用大偏差的经典求法,得到了随机变量的非随机和和随机和的大偏差表达式,推广了独立同分布情形下的相关结论.     

NA及B-值随机变量序列的平均移动过程的大偏差原理

本文在比较一般的条件下建立了两个大偏差原理：平稳NA随机变量序列的平均移动过程的大偏差原理和独立同分布的B-值随机变量序列的平均移动过程的大偏差原理。     

退火过程的轨道性质

本文中我们建立了一些非时齐过程的大偏差性质．利用大偏差技术，我们找到了退火过程的ω－极限集．     

宽上限相依的随机变量和的精确大偏差

通过研究了长尾上的带宽上限相依的随机变量和的精确大偏差,利用经典大偏差的方法,得到了非随机和和随机和的两种渐近结果.     

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.     

特殊重尾随机变量随机和的大偏差

文献[1]对于一些经典重尾随机变量的随机和大偏差作了有意义的讨论,本文则讨论了另外一些同样有用的重尾随机和的大偏差.     

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.     

部分转移风险过程的大偏差

本文研究了部分转移风险过程的大偏差问题.利用构造指数鞅的方法,得到了部分转移风险过程的大偏差.该结果给出部分转移风险过程的一个渐近行为.     

矩阵值Ornstein-Uhlenbeck过程的大偏差上界（英文）

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.     

回归函数的最近邻估计之大偏差概率的指数率

设(X,Y)是取值于 R~d×R~1 的随机变量,其 X 的边缘分布为 v,Y 关于 X 的条件分布函数为 F(y|x).于是变量 Y 关于 X 的回归函数即条件期望为r(x)=∫_(R~1)ydF(y|x).(1.1)设(X_1,Y_1),…,(X_n,Y_n)是(X,Y) 的一组独立观测值,或称为(X,Y)的一组样本.对固定的 x∈R~d,记(R_(1,x)~(?),…,R_(n,x)~(?)为(1,…,n)的一个随机置换,     

Large deviations for perturbed reflected diffusion processes

In this article, we establish a large deviation principle for the solutions of perturbed reflected diffusion processes. The key is to prove a uniform Freidlin–Ventzell estimate of perturbed diffusion processes.     

Generalized calculus and sdes with non regular drift

In this note we prove a precise asymptotic estimate for Laplace type functionals for a parabolic SPDE. We use a large deviation principle, the stochastic Taylor expansion, some exponential inequalities and support theorems for our stochastic partial differential equation     

Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

In this paper, we study the existence-uniqueness and large deviation estimate for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then we apply them to a large class of semilinear stochastic partial differential equations (SPDE), and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Moreover, stochastic Navier-Stokes equations are also investigated.     

金融资产收益率尾概率估计研究

在对金融资产进行投资时,投资者所关注的问题往往是金融资产收益率发生大波动的概率,简称尾概率.本文利用大偏差定理对此概率如何进行估计进行深入研究.将收益率按其尾部的分布特征分成三类,分别对其进行研究,得到三种不同的估计公式.本文对收益率序列存在相关性、收益率是多元随机变量情况下的尾概率估计问题也进行了分析.     

Large deviation theorem for Hill's estimator

To estimate the exponent of a regularly varying d.f. F, the asymptotic behaviour of Hill's estimator has been extensively discussed. Under the assumption that the d.f. F is continuous, we obtain the large deviation theorem for Hill's estimator. Project supported by the National Natural Science Foundation of China     

Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations

The estimate of the probability of the large deviation or the statistical random field is the key to ensure the convergence of moments of the associated estimator, and it also plays an essential role to prove mathematical validity of the asymptotic expansion of the estimator. For non-linear stochastic processes, it involves technical difficulties to show a standard exponential type estimate; besides, it is not necessary for these purposes. In this paper, we propose a polynomial-type large deviation inequality which is easily verified by the L ^p -boundedness of certain functionals; usually they are simple additive functionals. We treat a statistical random field with multi-grades and discuss M and Bayesian type estimators. As an application, we show the behavior of those estimators, including convergence of moments, for the statistical random field in the quasi-likelihood analysis of the stochastic differential equation that is possibly multi-dimensional and non-linear. The results are new even for stochastic differential equations, while they obviously apply to other various statistical models.     

平稳NA随机变量序列中偏差的下界估计

本文在比较一般的条件下得到了平稳NA序列的中偏差下界估计，进而得到平稳NA序列的中偏差原理。     

Estimate of Distributions of Sums of Independent Random Variables

We investigate necessary and sufficient conditions under which one estimate of exponential type is valid for large deviation probabilities of sums of independent identically distributed random variables. Bibliography: 3 titles.