Limit Processes for Age-Dependent Branching Particle Systems

We consider systems of spatially distributed branching particles in R ^d . The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on R ^d of a superprocess in R ₊×R ^d . The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles.     

Ratio limit theorems for branching Ornstein-Uhlenbeck processes

We prove ratio limit theorems for critical ano supercritical branching Ornstein-Uhlenbeck processes. A finite first moment of the offspring distribution {p_n} assures convergence in probability for supercritical processes and conditional convergence in probability for critical processes. If even Σp_nnlog⁺log⁺n< ∞, then almost sure convergence obtains in the supercritical case.     

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首先, 当$Q$是一个拟单调的q矩阵的时候, 我们找出最小的$Q$函数是一个Feller的转移函数的准则. 然后我们把这个结论应用于生成分支q矩阵并得到相应的生成分支过程的Feller准则. 特别地, 设$\theta$是分支q矩阵中的非线性数, 总是存在一个分点$\theta_0$满足$1\leq\theta_0\leq2$或$\theta_0<+\infty$使得 生成分支过程是否是Feller的要依据$\theta<\theta_0$或者$\theta>\theta_0$.     

Uniform Asymptotic Expansion of Likelihood Ratio for Markov Dependent Observations

An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test.     

两个总体相等的广义似然比检验

利用广义似然比检验的原理,首先求出广义似然比统计量的极限分布,然后给出了两个总体相等的广义似然比检验方法,并且给出了随机模拟结果.     

Uniqueness and Extinction of Weighted Markov Branching Processes

This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80     

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.     

Sharp Error Estimate for Maximum Likelihood Estimator of Nonstationary Diffusion Processes

We consider the maximum likelihood estimator of the unknown parameter in a class of nonstationary diffusion processes. We give further a precise estimate for the error of the estimator.     

随机环境中多物种分枝游动质点密度矩阵的极限分布

本文研究了随机环境中的多物种分枝游动于时刻k,位置x的质点密度矩阵序列{M~(k)(x)}k>1的极限分布。我们在证明了M~(k)(x),k>1,x∈Z是k个独立同分布的矩阵值随机元的乘积的基础上,主要证明了随机序列{logM_(ij)~(k)(x)}k>1依某种意义规范后是渐近正态的。     

High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of points is a very challenging problem and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners. This article has supplementary material online.     

Robust Stabilization by Dynamic Combined State and Output Feedback Compensator for Nonlinear Systems with Jumps

This paper deals with the robustness of the class of nonlinear systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption that the Markovian jump process (disturbance) is irreducible and under complete access to the system state and its mode, we establish robust stability results in two cases: (i) under matching conditions; and (ii) under bounded uncertainties.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0036444     

Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations

In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure q^θ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe n + 1 data at t_iⁿ = ih_n, . We suppose h_n → 0, nh_n → ∞, nh_n² → 0. Final version 20 December 2004     

随机环境中两性分枝过程的马氏性和对偶性

证明了独立同分布环境中的两性分枝过程是时奇的马氏链,给出了过程灭绝一爆炸这一对偶性的一个新的证明。在随机环境情形下,证明了一类单调函数的存在性。     

方差未知时两样本正态混合模型齐-性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

方差未知时两样本正态混合模型齐一性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

有限混合模型有限制Log极大似然比统计量的极限分布

有限混合模型的Log极大似然比统计量极限分布不是平常x2分布,1985年已为Hartigan指出.在这篇文章我们限制了混合比大于一正数下,讨论了两个含单个未知参数混合模型的Log极大似然比统计量的极限分布,它是零与x2分布的混合分布.     

随机受控分支过程中繁衍变量均值的经验似然估计

文章研究受控分支过程在随机环境下的繁衍变量均值的估计问题.我们基于加权条件最小二乘法构造估计方程,发展了一个经验似然比检验,并证明了这个检验统计量的极限分布是χ^2分布.最后通过随机模拟验证了经验似然方法有较高的覆盖概率.     

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??Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

Diffusion Approximations for Queues with Markovian Bases

Consider a base family of state-dependent queues whose queue-length process can be formulated by a continuous-time Markov process. In this paper, we develop a piecewise-constant diffusion model for an enlarged family of queues, each of whose members has arrival and service distributions generalized from those of the associated queue in the base. The enlarged family covers many standard queueing systems with finite waiting spaces, finite sources and so on. We provide a unifying explicit expression for the steady-state distribution, which is consistent with the exact result when the arrival and service distributions are those of the base. The model is an extension as well as a refinement of the M/M/s-consistent diffusion model for the GI/G/s queue developed by Kimura [13] where the base was a birth-and-death process. As a typical base, we still focus on birth-and-death processes, but we also consider a class of continuous-time Markov processes with lower-triangular infinitesimal generators.     

Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin andLawlessucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and thedual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtainedby the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.