Bisexual Galton-Watson Branching Processes in Random Environments

In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.     

一维扩散过程的小随机扰动

本文考虑一维扩散过程的小随机扰动．我们应用随机分析方法，给出了当扰动趋于零时，平均越出时间的渐近估计和越出时间的概率估计．     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.     

随机环境中受控分枝过程的极限定理

讨论了随机环境中受控分枝过程{Z_n:n∈N}的极限问题.给出了过程在{S_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛、L~1收敛和L~2收敛的充分条件,以及过程{W:n∈N}的极限非退化于0的充分条件和必要条件,得到了过程在{I_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛和L~1收敛的充分条件.     

Estimation of Local Smoothness Coefficients for Continuous Time Processes

We consider processes that satisfied a local Hölder condition with coefficient ₀. According to the sampling times of observations given by i _n with i=0,...,n–1, we study two general classes of estimators for ₀. Their almost sure rates of convergence depend on asymptotic independence of the observed processes, on _n and eventually on an extra parameter ₀. Since this last parameter is in general unknown, we construct a family of preliminary estimators for ₀ with their rates of almost sure convergence. Finally we present some numerical simulations in order to compare the behaviour of our various estimators.     

基于离散观测下Cauchy-OU过程的最大似然估计

基于离散观测样本,本文研究Cauchy-OU过程的参数估计问题.在大多数情况下,离散时间的最大似然函数是不能直接计算出来的,因此采用傅里叶变换及Gaver-Stehfest算法,构造似然函数的一个显式逼近序列,且该序列收敛于真实(但未知)的似然函数.最后,采用最大似然估计法估计出未知参数.仿真实验表明,所得到的参数估计是比较准确且稳定的.     

独立平稳随机环境中的P—S—D分枝过程

本文研究了独立同分布的随机环境中的Ｐ－Ｓ－Ｄ分枝过程,获得了有关过程的渐近性态以及灭 绝概率的一些结果．     

Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields

We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral distribution and a positive and piecewise continuous spectral density. We obtain necessary and sufficient conditions on the regression sequences such that a linear estimator of the regression coefficients is asymptotically unbiased and mean square consistent. For such regression sequences the asymptotic covariance matrix of the linear least squares estimator of the regression coefficients is derived.     

连续型随机向量联合熵的离散方差分离估计

提出了一种"离散方差分离"法,用于连续型随机向量联合熵的估计.方法分为"方差分离"和"离散"两个步骤.前者通过分离"标准熵"与"标准差对数和"来避免维数灾害;后者通过各分量的"最佳分割数"来离散连续型随机向量,从而避开了联合密度估计.仿真实验表明:该方法以很低的计算复杂度,准确地逼近了理论值.     

On Some Path Properties of Symmetric Stable-Like Processes for One Dimension

We show that a symmetric stable-type form becomes a Dirichlet form in the wide sense under a quite mild assumption and give a necessary and sufficiently condition that the domain contains the family of all uniformly Lipschitz continuous functions with compact support. Moreover we give some path properties of the corresponding Markov processes (we call the processes symmetric stable-like processes) in one dimension such as exceptionality of points and recurrence of the processes. We then note that the recurrence of the processes depend on the behavior of the index functions at the infinity.     

L1-Norm Estimation and Random Weighting Method in a Semiparametric Model

In this paper, the L_1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L_1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method.     

Free Wishart Processes

Using a matrix approach, we define free Wishart processes of parameter > 0 and prove a free additivity property and invertibility for > 1. For 1, we show that a free Wishart process is a solution of a SDE of square Bessel process type, driven by a free complex Brownian motion. In the case > 1, we establish existence and uniqueness of a strong solution of such a SDE.     

响应变量随机缺失下的广义变系数模型的估计

在响应变量随机缺失时,利用拟似然方法给出了广义变系数模型中非参数函数系数的估计.研究了所得到的估计的渐近性质,求出了估计的渐近偏差与渐近方差,并进行模拟比较.     

Super-Tree Random Measures

We use supercritical branching processes with random walk steps of geometrically decreasing size to construct random measures. Special cases of our construction give close relatives of the super-(spherically symmetric stable) processes. However, other cases can produce measures with very smooth densities in any dimension.     

关于随机算子若干问题的研究

研究了新的随机不动点指数的计算问题,利用随机不动点指数的理论推广了著名的Amann定理.提出了随机算子的随机渐进歧点的新概念,并且研究了随机k(ω)-集压缩算子的随机渐进歧点的一些问题,也得到了若干新的结果.     

随机向量的函数的独立性的一个问题

给出了随机变量 X1,X2 ,X3 ,X4 每三个相互独立 ,但 X1±X2 与 X3 ± X4 不相互独立的例子 ,以及 X1,X2 ,X3 每两个相互独立 ,但 X1± X2 与 X3 不相互独立的例子 .     

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??This paper studies nonparametric estimation of the integratedvolatility of Poisson jump-diffusion processes with noisy high-frequency data. Wepropose jump-robust two-scale and multi-scale estimators. The estimators are based ona combination of the multi-scale method and threshold technique, which serves to removemicrostructure noise and jumps, respectively. Furthermore, asymptotic properties of theproposed estimators, such as consistency, are established.     

Divergence of a Random Walk Through Deterministic and Random Subsequences

Let {S _n} _n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n _i for which respectively We thereby obtain conditions for to be a strong limit point of {S _n} or {S _n /n}. The first of these properties is shown to be equivalent to for some sequence a _i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between and for an increasing function fand suitable sequences n _i and a _i. These sorts of properties are of interest in sequential analysis. Known conditions for and (divergence through the whole sequence n) are also simplified.     

基于Brewer抽样的不放回样本追加策略下域的估计

本文研究了基于Brewer抽样的不放回追加策略,给出单元的前两阶包含概率的具体计算公式,并构造联合设计下的Horvitz-Thompson估计,同时给出了模拟结果。根据模拟结果可以看出,在联合设计下域总量估计的精度比基本设计和追加设计下估计量的精度高。