随机环境中伴有移民且配对依赖人口数的两性分枝过程（英文）

本文首先介绍了两性分枝过程的发展情况,在前人研究的基础上,本文建立了更符合自然界两性生物繁衍规律的模型,配对依赖当前人口数且伴有移民的两性分枝过程.利用上可加函数的性质,得到了平均增长率的极限.在一定的条件,推导出此过程以概率1灭绝的一个充要条件,进而推广了前人的研究成果.     

随机环境下单边二重随机游动

为了研究随机环境下单边二重随机游动的极限问题,也即随机环境下含有反射壁的二重随机游动的极限问题,本文利用二重随机游动的首达时与分枝链的关系,给出了当随机环境平稳遍历时,在几乎处处的环境下该过程常返,正常返及大数定律的条件。     

二叉树上非齐次分支马氏链一类强极限定理

近年来树图或者树形网络等诸多复杂系统的结构性质与极限性质逐渐成为研究的热点问题,特别是在树指标马尔可夫链领域的研究中,国内外学者们取得了丰富的研究成果.二叉树上非齐次分支马尔可夫链作为一类特殊的树指标马尔可夫链,该模型的极限性质被国内外学者的广泛研讨并应用于生物动力学、信息论等诸多领域.本文致力于研究在有限状态空间空间取值的二叉树上非齐次分支马尔可夫链转移概率调和平均的极限性质以及该性质与树指标马尔可夫链模型之间的联系.首先在新的条件下,本文给出了在有限状态空间中取值的二叉树上非齐次分支马氏链的强极限定理,并进一步得到了其随机转移概率调和平均的强极限定理,最后借助于两类模型之间的等价关系以及平均值不等式,推广了树指标非齐次马氏链随机转移概率的极限定理。     

稳定分布吸引场中φ-混合随机变量序列加权和的极限性质

有关独立同分布随机变量序列加权和的强大数定律，已经有较完善的结果。近来陈平炎等人又研究了具有稳定分布的独立同分布随机变量序列的加权和的极限性质，而且得出有关φ-混合随机变量序列的重对数律。本文主要是讨论稳定分布吸引场中φ-混合序列加权和的极限性质，并给出相应的重对数律。     

m相依序列的样本分位数核估计的中偏差和大偏差

分位数是统计学中的一个重要概念,它在可靠性统计分析以及经济、金融、生物信息、医学等领域都有非常广泛的应用.相依随机序列削弱了独立性的限制,得到了众多关注和研究.因此,本文基于m相依序列,研究了样本分位数核估计的大样本性质.首先,利用m相依序列的极限理论,通过计算Cramer函数,证明了样本分位数核估计的中偏差原理.其次...     

采用面积坐标的四边形二次膜元

文献［１］［２］建立了四边形单元的面积坐标体系，本文在此基础上，利用优选的广义协调条件，构造了两个广义协调四边形单元，算例表明这两个单元是收敛的，可靠的。     

φ~混合序列部分和的收敛性质

设{Xn,n≥1)是~(φ)混合序列,利用随机变量的截尾方法和~(φ)混合序列的三级数定理,本文研究了~(φ)混合序列的性质,得到了矩条件下~(φ)混合序列的一类强极限定理和强大数定律,并给出了一些简单应用,推广了若干经典的强大数定律.     

参数扰动的RLC低通滤波器的随机共振

研究了RLC低通滤波器在电导受到非对称双值色噪声扰动时的随机共振现象．利用随机平均法和Shapiro—Loginov公式,得到了平均输出幅度增益的精确表达式．分析表明,在欠阻尼、临界阻尼和过阻尼RLC低通滤波器中,平均输出幅度增益对电导噪声的非对称性、相关时间、强度和信号频率都存在非单调依赖关系．适当的噪声和系统参数条件可以使有噪声时系统的平均输出幅度增益大于没有噪声时系统的平均输出幅度增益．噪声可以提高滤波器对高频信号的衰减率．恰当的条件可以获得平均输出幅度增益的最大值．     

间断雨量序列随机模拟的研究：暴雨洪水流域系统随机模拟研究之四

对间断雨量序列有雨、无雨状态的交替变化规律，本文沿用马尔可夫转移概率描述。对间断雨量的模拟，本文提出对不同状态，依据其条件雨量序刑的统计性质，分别采用不同的方法描述：①由无雨转到有雨时，有雨序列用一定概率分布刻划；②由有雨转到有雨时，若两个有雨序列之间是相关的，则采用某种相依随机模型表征，若是相互无关的，则后一个雨量序列也用一定概率分布刻划，实测雨量资料初步检验表明、该方法随机模拟间断雨量序列是成     

单种子和多种子对正态随机序列质量的影响

通常一个正态随机序列是由同一个种子生成的,然而实际上序列中的每一个随机数还可用不同的种子来产生。提出了多种子的产生方法以及连续调用随机数发生器时防止产生相同序列的措施,利用统计模拟和假设检验理论,采用四个不同的统计量从正态性、均值、方差、随机性这四个方面对单、多种子法在不同时间段生成的大量随机序列的质量进行了对比研究,结果表明,多种子法生成的随机序列在正态性和方差质量方面有明显的优势,而在均值和随机性方面,这两种方法的效果基本一致,故总的说来多种子法要优于单种子法。     

Weighted conditional least square estimators for bisexual branching processes with immigration

The aim of this paper is to study some inferential problems arising from the class of bisexual Galton–Watson branching processes with immigration of females and males (BGWPI). Immigrants are assumed to be unobservable, and it is only possible to sample the number of females, males, and couples (mating units) in each generation. Under these conditions, weighted conditional least square estimators are proposed for the offspring and immigration mean vectors. Asymptotic properties of such estimators are investigated when the process is subcritical and supercritical, paying especial attention to their strong consistency and limit distributions. Weighted conditional least square estimators are also developed for the offspring and immigration variance vectors, and their asymptotic properties are studied. Some comments on the critical case are also given to possibly provide a unified estimation theory for BGWPI.     

Bisexual branching processes with offspring and mating depending on the number of couples in the population

In this work, we introduce a discrete-time bisexual branching process which considers both offspring and mating depending on the number of couples in the population at the previous generation. For such a model, we determine several probabilistic properties and provide some theoretical results concerning its limiting evolution. As an illustration, some simulated examples are given.     

Limiting behaviour for superadditive bisexual Galton-Watson processes in varying environments

In this paper, the class of superadditive bisexual Galton-Watson processes in varying environments is considered and the limiting behaviour of the number of mating units per generation, suitably normalized, is investigated. Two sequences of normalizing constants are considered and, for each one of them, limit theorems are established. In particular, conditions for the almost sure,L ¹ andL ² convergence to a non degenerate at 0 random variable are determined. Research supported by the Consejería de Educación, Ciencia y Tecnología de la Junta de Extremadura and the Fondo Social Europeo, grant IPR00A056 and the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2000-0356.     

Bayesian estimation in the class of bisexual branching processes with population-size dependent mating

This paper deals with the class of bisexual branching processes with population-size dependent mating introduced in Molina et al. (2002, Bisexual Galton–Watson branching process with population-size dependent mating. J Appl Probab 39:479–490). We determine Bayes estimators for the main moments of such processes in both situations: assuming offspring distribution belonging to the bivariate power series family and considering that no assumption is made about the underlying offspring distribution. As illustration we provide several examples, in particular, considering some classical offspring distributions, we explicitly determine the proposed Bayes estimators and, through simulation, we show the evolution of their estimates and of the corresponding high posterior density credibility sets.      

Bayesian conjugate analysis of the Galton-Watson process

In this article we consider the Bayesian statistical analysis of a simple Galton-Watson process. Problems of interest include estimation of the offspring distribution, classification of the process, and prediction. We propose two simple analytic approximations to the posterior marginal distribution of the reproduction mean. This posterior distribution suffices to classify the process. In order to assess the accuracy of these approximations, a comparison is provided with a computationally more expensive approximation obtained via standard Monte Carlo techniques. Similarly, a fully analytic approximation to the predictive distribution of the future size of the population is discussed. Sampling-based and hybrid approximations to this distribution are also considered. Finally, we present some illustrative examples. The first author is supported by the Alberto Baillères Chair on Insurance and International Finance of ITAM. This work was partially supported by Sistema Nacional de Investigadores, Mexico.     

Estimacion no parametrica de la edad y de la probabilidad de extincion en procesos de Galton-Watson

Sumario Se proponen estimadores no paramétricos de la edad y de la probabilidad de extinción de un proceso de ramificación de Galton-Watson. Dichos estimadores son comparados por simulación de Monte-Carlo, con otros estimadores propuestos por Stigler (1970) y Grump and Howe (1972).

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Summary Nonparametric estimators of the age and the probability of extinction of a Galton-Watson branching process are given. A Monte-Carlo simulation shows that these estimators compare favourably with a estimators studied earlier by Stigler (1970) and Crump and Howe (1972).

     

Reliability properties of systems with exchangeable components and exponential conditional distributions

We study basic properties for bivariate systems with exchangeable components and exponential conditional distributions which represent bi-component biological or engineering systems with structural dependency. This is equivalent to suppose that we have similar components with the bivariate exponential conditional joint distribution defined by Arnold and Strauss (1988). Specifically, we study the reliability functions, the moments, some aging measures, ordering and classification properties for series and parallel systems. Supported by Ministerio de Ciencia y Tecnología under grant BFM2003-02947     

非齐次马氏链样本相对熵率存在定理

样本相对熵率是信息论中一个重要的内容,在统计假设检验及编码理论中起着非常重要的作用.本文的目的是要研究在有限状态空间中取值的非齐次马氏链样本相对熵率的存在性.首先将数列绝对平均收敛的定义推广到平面上,并得到平面点列绝对平均收敛的定义及相关引理,然后利用非齐次马氏链二元函数的一类平均极限定理及强大数定律,给出非齐次马氏链样本相对熵率存在的条件.本文将信息论中关于独立同分布随机变量序列的假设检验问题做了更为广泛的推广.     

A relative crack opening time correlation for corrosion fatigue crack growth in offshore structures

A considerable amount of research has been carried out on the prediction of mean stress effects on fatigue crack growth in structures. Newer types of structure are now being developed for use in highly dynamic, harsh marine environments, particularly for renewable energy applications. Therefore, the extent to which mean stresses can enhance corrosion‐assisted fatigue damage in these structures needs to be better understood. A new theoretical model that accounts for mean stress effects on corrosion fatigue crack growth is proposed. The model is developed based on the relative crack opening period per fatigue cycle and by considering only the damaging portion of the stress cycle. The baseline data for the modelling exercise are the data obtained at a stress ratio of 0.1 in air and seawater tests conducted on compact tension specimens. The model is validated by comparison with experimental data and with other fatigue crack propagation models. The proposed model correlates fairly well with experimental data and the other models examined.     

Synthesis of branched 'nanotrees' by controlled seeding of multiple branching events

The formation of nanostructures with controlled size and morphology has been the focus of intensive research in recent years. Such nanostructures are important in the development of nanoscale devices and in the exploitation of the properties of nanomaterials. Here we show how tree-like nanostructures ('nanotrees') can be formed in a highly controlled way. The process involves the self-assembled growth of semiconductor nanowires via the vapour-liquid-solid growth mode. This bottom-up method uses initial seeding by catalytic nanoparticles to form the trunk, followed by the sequential seeding of branching structures. Each level of branching is controlled in terms of branch length, diameter and number, as well as chemical composition. We show, by high-resolution transmission electron microscopy, that the branching mechanism gives continuous crystalline (monolithic) structures throughout the extended and complex tree-like structures. The controlled seeding method that we report here has potential as a generic means of forming complex branching structures, and may also offer opportunities for applications, such as the mimicking of photosynthesis in nanotrees.